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Theorem 3orel13 30134
Description: Elimination of two disjuncts in a triple disjunction. (Contributed by Scott Fenton, 9-Jun-2011.)
Assertion
Ref Expression
3orel13  |-  ( ( -.  ph  /\  -.  ch )  ->  ( ( ph  \/  ps  \/  ch )  ->  ps ) )

Proof of Theorem 3orel13
StepHypRef Expression
1 3orel3 30129 . 2  |-  ( -. 
ch  ->  ( ( ph  \/  ps  \/  ch )  ->  ( ph  \/  ps ) ) )
2 orel1 383 . 2  |-  ( -. 
ph  ->  ( ( ph  \/  ps )  ->  ps ) )
31, 2sylan9r 662 1  |-  ( ( -.  ph  /\  -.  ch )  ->  ( ( ph  \/  ps  \/  ch )  ->  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 369    /\ wa 370    \/ w3o 981
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 188  df-or 371  df-an 372  df-3or 983
This theorem is referenced by:  soseq  30276  nodenselem8  30359
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