Theorem bj-cbvexvv

Description: Existentially quantifying with respect to a non-occurring variable is independent of that variable, over ax-1 -- ax-5 and the existence axiom extru . (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		ax-5	|- ( ps -> A. x ps )
3	1 2	syl	|- ( E. y ps -> A. x ps )
4		bj-axdd2	|- ( E. x ph -> ( A. x ps -> E. x ps ) )
5	3 4	syl5	|- ( E. x ph -> ( E. y ps -> E. x ps ) )