Theorem bj-sbievwd

Description: Variant of sbievw . (Contributed by BJ, 7-Oct-2024)

	Ref	Expression
Hypotheses	bj-sbievwd.nf0	|- ( ph -> A. x ph )
	bj-sbievwd.nf	|- ( ph -> F// x ch )
	bj-sbievwd.is	|- ( ( ph /\ x = y ) -> ( ps <-> ch ) )
Assertion	bj-sbievwd	|- ( ph -> ( [ y / x ] ps <-> ch ) )

Proof

Step	Hyp	Ref	Expression
1		bj-sbievwd.nf0	|- ( ph -> A. x ph )
2		bj-sbievwd.nf	|- ( ph -> F// x ch )
3		bj-sbievwd.is	|- ( ( ph /\ x = y ) -> ( ps <-> ch ) )
4		sb6	|- ( [ y / x ] ps <-> A. x ( x = y -> ps ) )
5	1 2 3	bj-equsalvwd	|- ( ph -> ( A. x ( x = y -> ps ) <-> ch ) )
6	4 5	syl5bb	|- ( ph -> ( [ y / x ] ps <-> ch ) )