Metamath Proof Explorer

Theorem bj-nfdt0

Description: A theorem close to a closed form of nf5d and nf5dh . (Contributed by BJ, 2-May-2019)

Ref Expression
Assertion bj-nfdt0 
|- ( A. x ( ph -> ( ps -> A. x ps ) ) -> ( A. x ph -> F/ x ps ) )

Proof

Step Hyp Ref Expression
1 alim 
 |-  ( A. x ( ph -> ( ps -> A. x ps ) ) -> ( A. x ph -> A. x ( ps -> A. x ps ) ) )
2 nf5 
 |-  ( F/ x ps <-> A. x ( ps -> A. x ps ) )
3 1 2 syl6ibr 
 |-  ( A. x ( ph -> ( ps -> A. x ps ) ) -> ( A. x ph -> F/ x ps ) )