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Theorem pm2.65 172
Description: Theorem *2.65 of [WhiteheadRussell] p. 107. Proof by contradiction. (Contributed by NM, 21-Jun-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 24 . 2  |-  ( (
ph  ->  ps )  -> 
( -.  ph  ->  -. 
ph ) )
2 con3 134 . 2  |-  ( (
ph  ->  ps )  -> 
( -.  ps  ->  -. 
ph ) )
31, 2jad 162 1  |-  ( (
ph  ->  ps )  -> 
( ( ph  ->  -. 
ps )  ->  -.  ph ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  pm4.82  926  lptioo2  31201  lptioo1  31202
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