ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm2.53 Unicode version

Theorem pm2.53 674
Description: Theorem *2.53 of [WhiteheadRussell] p. 107. This holds intuitionistically, although its converse does not (see pm2.54dc 826). (Contributed by NM, 3-Jan-2005.) (Revised by NM, 31-Jan-2015.)
Assertion
Ref Expression
pm2.53  |-  ( (
ph  \/  ps )  ->  ( -.  ph  ->  ps ) )

Proof of Theorem pm2.53
StepHypRef Expression
1 pm2.24 584 . 2  |-  ( ph  ->  ( -.  ph  ->  ps ) )
2 ax-1 5 . 2  |-  ( ps 
->  ( -.  ph  ->  ps ) )
31, 2jaoi 669 1  |-  ( (
ph  \/  ps )  ->  ( -.  ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ 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-in2 578  ax-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  ori  675  ord  676  orel1  677  pm2.63  747  notnotrdc  787  dfordc  827  pm5.6r  872  xorbin  1318  19.33b2  1563  onsucelsucexmid  4319  oprabidlem  5637  xnn0nnn0pnf  8682  absle  10417
  Copyright terms: Public domain W3C validator