diff --git a/qiskit/circuit/library/standard_gates/equivalence_library.py b/qiskit/circuit/library/standard_gates/equivalence_library.py
index 6bda41addc7c..5a519bf520e3 100644
--- a/qiskit/circuit/library/standard_gates/equivalence_library.py
+++ b/qiskit/circuit/library/standard_gates/equivalence_library.py
@@ -73,6 +73,7 @@
     ECRGate,
     ZGate,
     CZGate,
+    IGate,
     CCZGate,
     XXPlusYYGate,
     XXMinusYYGate,
@@ -170,6 +171,27 @@
 def_r.append(U3Gate(theta, phi - pi / 2, -phi + pi / 2), [q[0]])
 _sel.add_equivalence(RGate(theta, phi), def_r)
 
+# IGate
+q = QuantumRegister(1, "q")
+def_id = QuantumCircuit(q)
+def_id.append(UGate(0, 0, 0), [q[0]])
+_sel.add_equivalence(IGate(), def_id)
+
+q = QuantumRegister(1, "q")
+def_id_rx = QuantumCircuit(q)
+def_id_rx.append(RXGate(0), [q[0]])
+_sel.add_equivalence(IGate(), def_id_rx)
+
+q = QuantumRegister(1, "q")
+def_id_ry = QuantumCircuit(q)
+def_id_ry.append(RYGate(0), [q[0]])
+_sel.add_equivalence(IGate(), def_id_ry)
+
+q = QuantumRegister(1, "q")
+def_id_rz = QuantumCircuit(q)
+def_id_rz.append(RZGate(0), [q[0]])
+_sel.add_equivalence(IGate(), def_id_rz)
+
 # RCCXGate
 #
 #      ┌───────┐
diff --git a/test/python/transpiler/test_basis_translator.py b/test/python/transpiler/test_basis_translator.py
index 2f2fc146b9f5..970704bba701 100644
--- a/test/python/transpiler/test_basis_translator.py
+++ b/test/python/transpiler/test_basis_translator.py
@@ -928,22 +928,19 @@ def test_cx_bell_to_ecr(self):
         in_dag = circuit_to_dag(bell)
         out_dag = BasisTranslator(std_eqlib, ["ecr", "u"]).run(in_dag)
 
-        #         ┌────────────┐   ┌─────────────┐┌──────┐┌──────────┐
-        # q_0: ───┤ U(π/2,0,π) ├───┤ U(0,0,-π/2) ├┤0     ├┤ U(π,0,π) ├
-        #      ┌──┴────────────┴──┐└─────────────┘│  Ecr │└──────────┘
-        # q_1: ┤ U(-π/2,-π/2,π/2) ├───────────────┤1     ├────────────
-        #      └──────────────────┘               └──────┘
-
         qr = QuantumRegister(2, "q")
         expected = QuantumCircuit(2)
         expected.u(pi / 2, 0, pi, qr[0])
         expected.u(0, 0, -pi / 2, qr[0])
-        expected.u(-pi / 2, -pi / 2, pi / 2, qr[1])
+        expected.u(pi, 0, 0, qr[0])
+        expected.u(pi / 2, -pi / 2, pi / 2, qr[1])
         expected.ecr(0, 1)
-        expected.u(pi, 0, pi, qr[0])
         expected_dag = circuit_to_dag(expected)
 
         self.assertEqual(out_dag, expected_dag)
+        self.assertEqual(
+            Operator.from_circuit(bell), Operator.from_circuit(dag_to_circuit(out_dag))
+        )
 
     def test_cx_bell_to_cp(self):
         """Verify we can translate a CX bell to CP,U."""