Theorem bj-wnfanf

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

	Ref	Expression
Assertion	bj-wnfanf	|- ( ( E. x ph -> A. x ps ) -> A. x ( ph -> A. x 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-19.23bit	|- ( ( E. x ph -> A. x ps ) -> ( ph -> A. x ps ) )
3	1 2	sylg	|- ( ( E. x ph -> A. x ps ) -> A. x ( ph -> A. x ps ) )