Metamath Proof Explorer

Theorem bj-nexdvt

Description: Closed form of nexdv . (Contributed by BJ, 20-Oct-2019)

Ref Expression
Assertion bj-nexdvt 
|- ( A. x ( ph -> -. ps ) -> ( ph -> -. E. x ps ) )

Proof

Step Hyp Ref Expression
1 nfv 
 |-  F/ x ph
2 bj-nexdt 
 |-  ( F/ x ph -> ( A. x ( ph -> -. ps ) -> ( ph -> -. E. x ps ) ) )
3 1 2 ax-mp 
 |-  ( A. x ( ph -> -. ps ) -> ( ph -> -. E. x ps ) )