MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm2.65 Unicode version

Theorem pm2.65 166
Description: Theorem *2.65 of [WhiteheadRussell] p. 107. Proof by contradiction. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 8-Mar-2013.)
Assertion
Ref Expression
pm2.65  |-  ( (
ph  ->  ps )  -> 
( ( ph  ->  -. 
ps )  ->  -.  ph ) )

Proof of Theorem pm2.65
StepHypRef Expression
1 idd 23 . 2  |-  ( (
ph  ->  ps )  -> 
( -.  ph  ->  -. 
ph ) )
2 con3 128 . 2  |-  ( (
ph  ->  ps )  -> 
( -.  ps  ->  -. 
ph ) )
31, 2jad 156 1  |-  ( (
ph  ->  ps )  -> 
( ( ph  ->  -. 
ps )  ->  -.  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6
This theorem is referenced by:  pm4.82  899
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
  Copyright terms: Public domain W3C validator