Metamath Proof Explorer


Theorem bj-nnfad

Description: Nonfreeness implies the equivalent of ax-5 , deduction form. See nf5rd . (Contributed by BJ, 2-Dec-2023)

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 ) )