diff --git a/netkat/symbolic_packet.cc b/netkat/symbolic_packet.cc
index 42003fd..23ca3ef 100644
--- a/netkat/symbolic_packet.cc
+++ b/netkat/symbolic_packet.cc
@@ -79,7 +79,9 @@ bool SymbolicPacketManager::IsFullSet(SymbolicPacket packet) const {
 
 const SymbolicPacketManager::DecisionNode& SymbolicPacketManager::GetNodeOrDie(
     SymbolicPacket packet) const {
-  CHECK_LT(packet.node_index_, nodes_.size());  // Crash ok
+  CHECK_LT(packet.node_index_, nodes_.size())
+      << "Did you call this function on a leaf node (i.e. FullSet() or "
+         "EmptySet())? ";  // Crash ok
   return nodes_[packet.node_index_];
 }
 
@@ -335,6 +337,48 @@ SymbolicPacket SymbolicPacketManager::Xor(SymbolicPacket left,
   return Or(And(Not(left), right), And(left, Not(right)));
 }
 
+SymbolicPacket SymbolicPacketManager::Exists(absl::string_view field,
+                                             SymbolicPacket packet) {
+  if (IsFullSet(packet) || IsEmptySet(packet)) return packet;
+
+  // Compute result the hard way.
+  const DecisionNode node = GetNodeOrDie(packet);
+  std::string node_field = field_manager_.GetFieldName(node.field);
+
+  // Case 1: `packet` is a member of `Exists(field, *)`: remove the current node
+  // and return the OR-ing of all branches.
+  if (node_field == field) {
+    SymbolicPacket result_packet = node.default_branch;
+    for (const auto& [_, branch] : node.branch_by_field_value) {
+      result_packet = Or(result_packet, branch);
+    }
+    return result_packet;
+  }
+
+  // Case 2: calls `packet` is a member of `Exists(field, *)` for all it's
+  // branches: keep current node and call `Exists` on all branches and exclude a
+  // branch if it is the same as the default branch.
+  SymbolicPacket default_branch = Exists(field, node.default_branch);
+  absl::FixedArray<std::pair<int, SymbolicPacket>>
+      non_default_branches_by_field_value(node.branch_by_field_value.size());
+  int num_branches = 0;
+  for (const auto& [value, branch] : node.branch_by_field_value) {
+    SymbolicPacket non_default_branch = Exists(field, branch);
+    if (non_default_branch == default_branch) continue;
+    non_default_branches_by_field_value[num_branches++] =
+        std::make_pair(value, non_default_branch);
+  }
+
+  return NodeToPacket(DecisionNode{
+      .field = node.field,
+      .default_branch = default_branch,
+      .branch_by_field_value{
+          non_default_branches_by_field_value.begin(),
+          non_default_branches_by_field_value.begin() + num_branches,
+      },
+  });
+}
+
 std::string SymbolicPacketManager::ToString(SymbolicPacket packet) const {
   std::string result;
   std::queue<SymbolicPacket> work_list{{packet}};
diff --git a/netkat/symbolic_packet.h b/netkat/symbolic_packet.h
index 6f11fbf..2062066 100644
--- a/netkat/symbolic_packet.h
+++ b/netkat/symbolic_packet.h
@@ -227,6 +227,10 @@ class SymbolicPacketManager {
   // set, but not in both. Also known as symmetric set difference.
   SymbolicPacket Xor(SymbolicPacket left, SymbolicPacket right);
 
+  // Return the set of packets whose given `field` gets satisfied by some
+  // predicate.
+  SymbolicPacket Exists(absl::string_view field, SymbolicPacket packet);
+
   // Returns a human-readable string representation of the given `packet`,
   // intended for debugging.
   [[nodiscard]] std::string ToString(SymbolicPacket packet) const;
diff --git a/netkat/symbolic_packet_test.cc b/netkat/symbolic_packet_test.cc
index 413028f..1db2005 100644
--- a/netkat/symbolic_packet_test.cc
+++ b/netkat/symbolic_packet_test.cc
@@ -21,7 +21,6 @@
 
 #include "absl/base/no_destructor.h"
 #include "absl/container/flat_hash_map.h"
-#include "absl/container/flat_hash_set.h"
 #include "absl/strings/str_cat.h"
 #include "absl/strings/str_split.h"
 #include "absl/strings/string_view.h"
@@ -331,5 +330,32 @@ void XorIsAssociative(const PredicateProto& a, const PredicateProto& b,
 }
 FUZZ_TEST(SymbolicPacketManagerTest, XorIsAssociative);
 
+TEST(SymbolicPacketManagerTest, ExistsOnPacketWithSingleFieldReturnsFullSet) {
+  const std::string field = "a";
+  EXPECT_EQ(Manager().Exists(field, Manager().Compile(MatchProto(field, 3))),
+            Manager().FullSet());
+}
+
+TEST(SymbolicPacketManagerTest, ExistOnFieldRemovesPacketFieldProperty) {
+  const std::string field = "a";
+  constexpr int value = 3;
+  // p = (a=3 && b=4) || (b!=5 && c=5)
+  SymbolicPacket symbolic_packet = Manager().Compile(
+      OrProto(AndProto(MatchProto(field, value), MatchProto("b", 4)),
+              AndProto(NotProto(MatchProto("b", 5)), MatchProto("c", 5))));
+  SymbolicPacket symbolic_packet_without_field =
+      Manager().Exists(field, symbolic_packet);
+  EXPECT_FALSE(Manager().Contains(symbolic_packet_without_field,
+                                  Packet{{field, value}}));
+}
+
+TEST(SymbolicPacketManagerTest, ExistsOnFieldNotInPacketIsIdentity) {
+  // p = (a=3 && b=4) || (b!=5 && c=5)
+  SymbolicPacket symbolic_packet = Manager().Compile(
+      OrProto(AndProto(MatchProto("a", 3), MatchProto("b", 4)),
+              AndProto(NotProto(MatchProto("b", 5)), MatchProto("c", 5))));
+  EXPECT_EQ(symbolic_packet, Manager().Exists("d", symbolic_packet));
+}
+
 }  // namespace
 }  // namespace netkat