Theorem bj-wnf2

Description: When ph is substituted for ps , this is the first half of nonfreness ( . -> A. ) of the weak form of nonfreeness ( E. -> A. ) . (Contributed by BJ, 9-Dec-2023)

	Ref	Expression
Assertion	bj-wnf2	|- ( E. x ( E. x ph -> A. x ps ) -> ( E. x ph -> A. x ps ) )

Proof

Step	Hyp	Ref	Expression
1		hbe1	|- ( E. x ph -> A. x E. x ph )
2		bj-eximcom	|- ( E. x ( E. x ph -> A. x ps ) -> ( A. x E. x ph -> E. x A. x ps ) )
3		hbe1a	|- ( E. x A. x ps -> A. x ps )
4	1 2 3	syl56	|- ( E. x ( E. x ph -> A. x ps ) -> ( E. x ph -> A. x ps ) )