Metamath Proof Explorer


Theorem axc5c711toc5

Description: Rederivation of ax-c5 from axc5c711 . Only propositional calculus is used by the rederivation. (Contributed by NM, 19-Nov-2006) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion axc5c711toc5
|- ( A. x ph -> ph )

Proof

Step Hyp Ref Expression
1 ax-1
 |-  ( A. x ph -> ( A. x A. x -. A. x A. x ph -> A. x ph ) )
2 axc5c711
 |-  ( ( A. x A. x -. A. x A. x ph -> A. x ph ) -> ph )
3 1 2 syl
 |-  ( A. x ph -> ph )