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Theorem 3orel1 23465
Description: Partial elimination of a triple disjunction by denial of a disjunct. (Contributed by Scott Fenton, 26-Mar-2011.)
Assertion
Ref Expression
3orel1  |-  ( -. 
ph  ->  ( ( ph  \/  ps  \/  ch )  ->  ( ps  \/  ch ) ) )

Proof of Theorem 3orel1
StepHypRef Expression
1 3orass 939 . 2  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ph  \/  ( ps  \/  ch ) ) )
2 orel1 373 . 2  |-  ( -. 
ph  ->  ( ( ph  \/  ( ps  \/  ch ) )  ->  ( ps  \/  ch ) ) )
31, 2syl5bi 210 1  |-  ( -. 
ph  ->  ( ( ph  \/  ps  \/  ch )  ->  ( ps  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6    \/ wo 359    \/ w3o 935
This theorem is referenced by:  3orel2  23466
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-or 361  df-3or 937
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