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Metamath Proof Explorer

Theorem bj-19.37im

Description: One direction of 19.37 from the same axioms as 19.37imv . (Contributed by BJ, 2-Dec-2023)

Ref Expression
Assertion bj-19.37im 
|- ( F// x ph -> ( E. x ( ph -> ps ) -> ( ph -> E. x ps ) ) )

Proof

Step Hyp Ref Expression
1 19.35 
 |-  ( E. x ( ph -> ps ) <-> ( A. x ph -> E. x ps ) )
2 bj-nnfa 
 |-  ( F// x ph -> ( ph -> A. x ph ) )
3 2 imim1d 
 |-  ( F// x ph -> ( ( A. x ph -> E. x ps ) -> ( ph -> E. x ps ) ) )
4 1 3 biimtrid 
 |-  ( F// x ph -> ( E. x ( ph -> ps ) -> ( ph -> E. x ps ) ) )