Theorem bj-wnfenf

Description: When ph is substituted for ps , this statement expresses that weak nonfreeness implies the existential form of nonfreeness. (Contributed by BJ, 9-Dec-2023)

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

Proof

Step	Hyp	Ref	Expression
1		bj-wnf1	|- ( ( E. x ph -> A. x ps ) -> A. x ( E. x ph -> A. x ps ) )
2		bj-19.21bit	|- ( ( E. x ph -> A. x ps ) -> ( E. x ph -> ps ) )
3	1 2	sylg	|- ( ( E. x ph -> A. x ps ) -> A. x ( E. x ph -> ps ) )