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Metamath Proof Explorer

Theorem 19.36imv

Description: One direction of 19.36v that can be proven without ax-6 . (Contributed by Rohan Ridenour, 16-Apr-2022) (Proof shortened by Wolf Lammen, 22-Sep-2024)

Ref Expression
Assertion 19.36imv 
|- ( E. x ( ph -> ps ) -> ( A. x ph -> ps ) )

Proof

Step Hyp Ref Expression
1 pm2.27 
 |-  ( ph -> ( ( ph -> ps ) -> ps ) )
2 1 aleximi 
 |-  ( A. x ph -> ( E. x ( ph -> ps ) -> E. x ps ) )
3 ax5e 
 |-  ( E. x ps -> ps )
4 2 3 syl6com 
 |-  ( E. x ( ph -> ps ) -> ( A. x ph -> ps ) )