Theorem nf5-1

Description: One direction of nf5 can be proved with a smaller footprint on axiom usage. (Contributed by Wolf Lammen, 16-Sep-2021)

	Ref	Expression
Assertion	nf5-1	|- ( A. x ( ph -> A. x ph ) -> F/ x ph )

Proof

Step	Hyp	Ref	Expression
1		exim	|- ( A. x ( ph -> A. x ph ) -> ( E. x ph -> E. x A. x ph ) )
2		hbe1a	|- ( E. x A. x ph -> A. x ph )
3	1 2	syl6	|- ( A. x ( ph -> A. x ph ) -> ( E. x ph -> A. x ph ) )
4	3	nfd	|- ( A. x ( ph -> A. x ph ) -> F/ x ph )