Theorem eqvinc

Description: A variable introduction law for class equality. (Contributed by NM, 14-Apr-1995) (Proof shortened by Andrew Salmon, 8-Jun-2011) (Proof shortened by Thierry Arnoux, 23-Jan-2022)

	Ref	Expression
Hypothesis	eqvinc.1	|- A e. _V
Assertion	eqvinc	|- ( A = B <-> E. x ( x = A /\ x = B ) )

Proof

Step	Hyp	Ref	Expression
1		eqvinc.1	|- A e. _V
2		eqvincg	|- ( A e. _V -> ( A = B <-> E. x ( x = A /\ x = B ) ) )
3	1 2	ax-mp	|- ( A = B <-> E. x ( x = A /\ x = B ) )