Users' Mathboxes Mathbox for Rodolfo Medina < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  pm5.31r Unicode version

Theorem pm5.31r 26820
Description: Variant of pm5.31 571. (Contributed by Rodolfo Medina, 15-Oct-2010.)
Assertion
Ref Expression
pm5.31r  |-  ( ( ch  /\  ( ph  ->  ps ) )  -> 
( ph  ->  ( ch 
/\  ps ) ) )

Proof of Theorem pm5.31r
StepHypRef Expression
1 pm3.2 434 . . 3  |-  ( ch 
->  ( ps  ->  ( ch  /\  ps ) ) )
21imim2d 48 . 2  |-  ( ch 
->  ( ( ph  ->  ps )  ->  ( ph  ->  ( ch  /\  ps ) ) ) )
32imp 418 1  |-  ( ( ch  /\  ( ph  ->  ps ) )  -> 
( ph  ->  ( ch 
/\  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
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 177  df-an 360
  Copyright terms: Public domain W3C validator