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Theorem pm2.53 696
Description: Theorem *2.53 of [WhiteheadRussell] p. 107. This holds intuitionistically, although its converse does not (see pm2.54dc 861). (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 pm2.24 595 . 2  |-  ( ph  ->  ( -.  ph  ->  ps ) )
2 ax-1 6 . 2  |-  ( ps 
->  ( -.  ph  ->  ps ) )
31, 2jaoi 690 1  |-  ( (
ph  \/  ps )  ->  ( -.  ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 682
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-in2 589  ax-io 683
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  ori  697  ord  698  orel1  699  pm2.63  774  notnotrdc  813  dfordc  862  pm5.6r  897  xorbin  1347  19.33b2  1593  onsucelsucexmid  4415  oprabidlem  5770  omnimkv  6998  xnn0nnn0pnf  9021  absle  10829
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