ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm5.13dc Unicode version

Theorem pm5.13dc 856
Description: An implication holds in at least one direction, where one proposition is decidable. Based on theorem *5.13 of [WhiteheadRussell] p. 123. (Contributed by Jim Kingdon, 30-Mar-2018.)
Assertion
Ref Expression
pm5.13dc  |-  (DECID  ps  ->  ( ( ph  ->  ps )  \/  ( ps  ->  ph ) ) )

Proof of Theorem pm5.13dc
StepHypRef Expression
1 pm5.14dc 855 1  |-  (DECID  ps  ->  ( ( ph  ->  ps )  \/  ( ps  ->  ph ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 664  DECID wdc 780
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in2 580  ax-io 665
This theorem depends on definitions:  df-bi 115  df-dc 781
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator