Theorem bj-vtoclg1fv

Description: Version of bj-vtoclg1f with a disjoint variable condition on x , V . This removes dependency on df-sb and df-clab . Prefer its use over bj-vtoclg1f when sufficient (in particular when V is substituted for _V ). (Contributed by BJ, 14-Sep-2019) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	bj-vtoclg1fv.nf	|- F/ x ps
	bj-vtoclg1fv.maj	|- ( x = A -> ( ph -> ps ) )
	bj-vtoclg1fv.min	|- ph
Assertion	bj-vtoclg1fv	|- ( A e. V -> ps )

Proof

Step	Hyp	Ref	Expression
1		bj-vtoclg1fv.nf	|- F/ x ps
2		bj-vtoclg1fv.maj	|- ( x = A -> ( ph -> ps ) )
3		bj-vtoclg1fv.min	|- ph
4		bj-elissetv	|- ( A e. V -> E. x x = A )
5	1 2 3	bj-exlimmpi	|- ( E. x x = A -> ps )
6	4 5	syl	|- ( A e. V -> ps )