Theorem bj-cbvexvv

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

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

Proof

Step	Hyp	Ref	Expression
1		ax5e	|- ( E. y ps -> ps )
2		bj-spvew	|- ( E. x ph -> ( ps <-> E. x ps ) )
3	2	biimpd	|- ( E. x ph -> ( ps -> E. x ps ) )
4	1 3	syl5	|- ( E. x ph -> ( E. y ps -> E. x ps ) )