MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  con1 Unicode version

Theorem con1 120
Description: Contraposition. Theorem *2.15 of [WhiteheadRussell] p. 102. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 12-Feb-2013.)
Assertion
Ref Expression
con1  |-  ( ( -.  ph  ->  ps )  ->  ( -.  ps  ->  ph ) )

Proof of Theorem con1
StepHypRef Expression
1 id 19 . 2  |-  ( ( -.  ph  ->  ps )  ->  ( -.  ph  ->  ps ) )
21con1d 116 1  |-  ( ( -.  ph  ->  ps )  ->  ( -.  ps  ->  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  con1b  323  ax12olem3  1870  nneob  6650  uzwo  10281  uzwoOLD  10282
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
  Copyright terms: Public domain W3C validator