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

Theorem xoror 1361
Description: XOR implies OR. (Contributed by BJ, 19-Apr-2019.)
Assertion
Ref Expression
xoror  |-  ( (
ph  \/_  ps )  ->  ( ph  \/  ps ) )

Proof of Theorem xoror
StepHypRef Expression
1 xoranor 1359 . 2  |-  ( (
ph  \/_  ps )  <->  ( ( ph  \/  ps )  /\  ( -.  ph  \/  -.  ps ) ) )
21simplbi 272 1  |-  ( (
ph  \/_  ps )  ->  ( ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 698    \/_ wxo 1357
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-xor 1358
This theorem is referenced by:  mtpxor  1408
  Copyright terms: Public domain W3C validator