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Metamath Proof Explorer

Theorem 19.37imv

Description: One direction of 19.37v that can be proven without ax-6 . (Contributed by Rohan Ridenour, 16-Apr-2022)

Ref Expression
Assertion 19.37imv 
|- ( E. x ( ph -> ps ) -> ( ph -> E. x ps ) )

Proof

Step Hyp Ref Expression
1 ax-5 
 |-  ( ph -> A. x ph )
2 19.35 
 |-  ( E. x ( ph -> ps ) <-> ( A. x ph -> E. x ps ) )
3 2 biimpi 
 |-  ( E. x ( ph -> ps ) -> ( A. x ph -> E. x ps ) )
4 1 3 syl5 
 |-  ( E. x ( ph -> ps ) -> ( ph -> E. x ps ) )