Metamath Proof Explorer


Theorem bj-nnfed

Description: Nonfreeness implies the equivalent of ax5e , deduction form. (Contributed by BJ, 2-Dec-2023)

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

Proof

Step Hyp Ref Expression
1 bj-nnfed.1
 |-  ( ph -> F// x ps )
2 bj-nnfe
 |-  ( F// x ps -> ( E. x ps -> ps ) )
3 1 2 syl
 |-  ( ph -> ( E. x ps -> ps ) )