MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  retbwax3 Unicode version

Theorem retbwax3 1494
Description: tbw-ax3 1473 rederived from merco1 1484. (Contributed by Anthony Hart, 17-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
retbwax3  |-  ( ( ( ph  ->  ps )  ->  ph )  ->  ph )

Proof of Theorem retbwax3
StepHypRef Expression
1 retbwax2 1487 . 2  |-  ( ph  ->  ( ph  ->  ph )
)
2 merco1lem7 1493 . 2  |-  ( (
ph  ->  ( ph  ->  ph ) )  ->  (
( ( ph  ->  ps )  ->  ph )  ->  ph ) )
31, 2ax-mp 8 1  |-  ( ( ( ph  ->  ps )  ->  ph )  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-tru 1325  df-fal 1326
  Copyright terms: Public domain W3C validator