Theorem bj-nnfai

Description: Nonfreeness implies the equivalent of ax-5 , inference form. See nf5ri . (Contributed by BJ, 22-Sep-2024)

	Ref	Expression
Hypothesis	bj-nnfai.1	|- F// x ph
Assertion	bj-nnfai	|- ( ph -> A. x ph )

Proof

Step	Hyp	Ref	Expression
1		bj-nnfai.1	|- F// x ph
2		bj-nnfa	|- ( F// x ph -> ( ph -> A. x ph ) )
3	1 2	ax-mp	|- ( ph -> A. x ph )