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Theorem pm3.2im 626
Description: In classical logic, this is just a restatement of pm3.2 138. In intuitionistic logic, it still holds, but is weaker than pm3.2. (Contributed by Mario Carneiro, 12-May-2015.)
Assertion
Ref Expression
pm3.2im  |-  ( ph  ->  ( ps  ->  -.  ( ph  ->  -.  ps )
) )

Proof of Theorem pm3.2im
StepHypRef Expression
1 pm2.27 40 . 2  |-  ( ph  ->  ( ( ph  ->  -. 
ps )  ->  -.  ps ) )
21con2d 613 1  |-  ( ph  ->  ( ps  ->  -.  ( ph  ->  -.  ps )
) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 603  ax-in2 604
This theorem is referenced by:  expi  627  jc  639  expt  646  imnan  679  dfandc  869
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