Theorem vtoclg

Description: Implicit substitution of a class expression for a setvar variable. (Contributed by NM, 17-Apr-1995) Avoid ax-12 . (Revised by SN, 20-Apr-2024)

	Ref	Expression
Hypotheses	vtoclg.1	|- ( x = A -> ( ph <-> ps ) )
	vtoclg.2	|- ph
Assertion	vtoclg	|- ( A e. V -> ps )

Proof

Step	Hyp	Ref	Expression
1		vtoclg.1	|- ( x = A -> ( ph <-> ps ) )
2		vtoclg.2	|- ph
3		elisset	|- ( A e. V -> E. x x = A )
4	2 1	mpbii	|- ( x = A -> ps )
5	4	exlimiv	|- ( E. x x = A -> ps )
6	3 5	syl	|- ( A e. V -> ps )