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Metamath Proof Explorer

Theorem bj-19.36im

Description: One direction of 19.36 from the same axioms as 19.36imv . (Contributed by BJ, 2-Dec-2023)

Ref Expression
Assertion bj-19.36im 
|- ( F// x ps -> ( E. x ( ph -> ps ) -> ( A. x ph -> ps ) ) )

Proof

Step Hyp Ref Expression
1 19.35 
 |-  ( E. x ( ph -> ps ) <-> ( A. x ph -> E. x ps ) )
2 bj-nnfe 
 |-  ( F// x ps -> ( E. x ps -> ps ) )
3 2 imim2d 
 |-  ( F// x ps -> ( ( A. x ph -> E. x ps ) -> ( A. x ph -> ps ) ) )
4 1 3 biimtrid 
 |-  ( F// x ps -> ( E. x ( ph -> ps ) -> ( A. x ph -> ps ) ) )