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Theorem orel2 678
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 pm2.21 580 . 2  |-  ( -. 
ph  ->  ( ph  ->  ps ) )
31, 2jaod 670 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:  biorfi  698  pm2.64  748  pm5.71dc  903  ecased  1281  19.30dc  1559  dveeq2  1738  prel12  3584  funun  4995
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