Theorem bj-nnfad

Description: Nonfreeness implies the equivalent of ax-5 , deduction form. See nf5rd . (Contributed by BJ, 2-Dec-2024)

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

Proof

Step	Hyp	Ref	Expression
1		bj-nnfad.1	|- ( ph -> F// x ps )
2		bj-nnfa	|- ( F// x ps -> ( ps -> A. x ps ) )
3	1 2	syl	|- ( ph -> ( ps -> A. x ps ) )