Theorem vtoclg1f

Description: Version of vtoclgf with one non-freeness hypothesis replaced with a disjoint variable condition, thus avoiding dependency on ax-11 and ax-13 . (Contributed by BJ, 1-May-2019)

	Ref	Expression
Hypotheses	vtoclg1f.nf	|- F/ x ps
	vtoclg1f.maj	|- ( x = A -> ( ph <-> ps ) )
	vtoclg1f.min	|- ph
Assertion	vtoclg1f	|- ( A e. V -> ps )

Proof

Step	Hyp	Ref	Expression
1		vtoclg1f.nf	|- F/ x ps
2		vtoclg1f.maj	|- ( x = A -> ( ph <-> ps ) )
3		vtoclg1f.min	|- ph
4		elisset	|- ( A e. V -> E. x x = A )
5	3 2	mpbii	|- ( x = A -> ps )
6	1 5	exlimi	|- ( E. x x = A -> ps )
7	4 6	syl	|- ( A e. V -> ps )