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Theorem 3orel3 29330
Description: Partial elimination of a triple disjunction by denial of a disjunct. (Contributed by Scott Fenton, 26-Mar-2011.)
Assertion
Ref Expression
3orel3  |-  ( -. 
ch  ->  ( ( ph  \/  ps  \/  ch )  ->  ( ph  \/  ps ) ) )

Proof of Theorem 3orel3
StepHypRef Expression
1 df-3or 972 . 2  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ( ph  \/  ps )  \/  ch ) )
2 orel2 381 . 2  |-  ( -. 
ch  ->  ( ( (
ph  \/  ps )  \/  ch )  ->  ( ph  \/  ps ) ) )
31, 2syl5bi 217 1  |-  ( -. 
ch  ->  ( ( ph  \/  ps  \/  ch )  ->  ( ph  \/  ps ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 366    \/ w3o 970
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-or 368  df-3or 972
This theorem is referenced by:  3orel13  29335  nobndup  29700
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