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

Theorem oranim 841
Description: Disjunction in terms of conjunction (DeMorgan's law). One direction of Theorem *4.57 of [WhiteheadRussell] p. 120. The converse does not hold intuitionistically but does hold in classical logic. (Contributed by Jim Kingdon, 25-Jul-2018.)
Assertion
Ref Expression
oranim  |-  ( (
ph  \/  ps )  ->  -.  ( -.  ph  /\ 
-.  ps ) )

Proof of Theorem oranim
StepHypRef Expression
1 pm4.56 840 . . 3  |-  ( ( -.  ph  /\  -.  ps ) 
<->  -.  ( ph  \/  ps ) )
21biimpi 118 . 2  |-  ( ( -.  ph  /\  -.  ps )  ->  -.  ( ph  \/  ps ) )
32con2i 590 1  |-  ( (
ph  \/  ps )  ->  -.  ( -.  ph  /\ 
-.  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 102    \/ wo 662
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-in1 577  ax-in2 578  ax-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  unssin  3210  prneimg  3574  ftpg  5379  xrlttri3  8948
  Copyright terms: Public domain W3C validator