Theorem bj-cbvalvv

Description: Universally quantifying over a non-occurring variable is independent of that variable, over ax-1 -- ax-5 and the existence axiom extru . See bj-cbvaw for a strengthening. (Contributed by BJ, 8-Mar-2026) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-cbvalvv	|- ( E. x ph -> ( A. x ps -> A. y ps ) )

Proof

Step	Hyp	Ref	Expression
1		bj-spvw	|- ( E. x ph -> ( ps <-> A. x ps ) )
2	1	biimprd	|- ( E. x ph -> ( A. x ps -> ps ) )
3		ax-5	|- ( ps -> A. y ps )
4	2 3	syl6	|- ( E. x ph -> ( A. x ps -> A. y ps ) )