ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm3.2im Unicode version

Theorem pm3.2im 599
Description: In classical logic, this is just a restatement of pm3.2 137. 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 39 . 2  |-  ( ph  ->  ( ( ph  ->  -. 
ps )  ->  -.  ps ) )
21con2d 587 1  |-  ( ph  ->  ( ps  ->  -.  ( ph  ->  -.  ps )
) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 577  ax-in2 578
This theorem is referenced by:  expi  600  jc  613  expt  616  imnan  657  dfandc  812
  Copyright terms: Public domain W3C validator