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Theorem orel2 700
Description: Elimination of disjunction by denial of a disjunct. Theorem *2.56 of [WhiteheadRussell] p. 107. (Contributed by NM, 12-Aug-1994.) (Proof shortened by Wolf Lammen, 5-Apr-2013.)
Assertion
Ref Expression
orel2  |-  ( -. 
ph  ->  ( ( ps  \/  ph )  ->  ps ) )

Proof of Theorem orel2
StepHypRef Expression
1 idd 21 . 2  |-  ( -. 
ph  ->  ( ps  ->  ps ) )
2 pm2.21 591 . 2  |-  ( -. 
ph  ->  ( ph  ->  ps ) )
31, 2jaod 691 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:  biorfi  720  pm2.64  775  stdcn  817  pm5.71dc  930  ecased  1312  19.30dc  1591  dveeq2  1771  prel12  3668  funun  5137
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