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Theorem orel1 679
Description: Elimination of disjunction by denial of a disjunct. Theorem *2.55 of [WhiteheadRussell] p. 107. (Contributed by NM, 12-Aug-1994.) (Proof shortened by Wolf Lammen, 21-Jul-2012.)
Assertion
Ref Expression
orel1  |-  ( -. 
ph  ->  ( ( ph  \/  ps )  ->  ps ) )

Proof of Theorem orel1
StepHypRef Expression
1 pm2.53 676 . 2  |-  ( (
ph  \/  ps )  ->  ( -.  ph  ->  ps ) )
21com12 30 1  |-  ( -. 
ph  ->  ( ( ph  \/  ps )  ->  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 664
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 580  ax-io 665
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  biorf  698  pm2.25dc  830  pm2.85dc  849  euor2  2006  prel12  3615  funun  5058  acexmidlema  5643  acexmidlemb  5644
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