ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm2.5dc Unicode version

Theorem pm2.5dc 853
Description: Negating an implication for a decidable antecedent. Theorem *2.5 of [WhiteheadRussell] p. 107 under a decidability condition. (Contributed by Jim Kingdon, 29-Mar-2018.)
Assertion
Ref Expression
pm2.5dc  |-  (DECID  ph  ->  ( -.  ( ph  ->  ps )  ->  ( -.  ph 
->  ps ) ) )

Proof of Theorem pm2.5dc
StepHypRef Expression
1 pm2.5gdc 852 1  |-  (DECID  ph  ->  ( -.  ( ph  ->  ps )  ->  ( -.  ph 
->  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4  DECID wdc 820
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699
This theorem depends on definitions:  df-bi 116  df-stab 817  df-dc 821
This theorem is referenced by:  pm5.11dc  895
  Copyright terms: Public domain W3C validator