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Theorem 3o3cs 23115
Description: Deduction eliminating disjunct. (Contributed by Thierry Arnoux, 19-Dec-2016.)
Hypothesis
Ref Expression
3o1cs.1  |-  ( (
ph  \/  ps  \/  ch )  ->  th )
Assertion
Ref Expression
3o3cs  |-  ( ch 
->  th )

Proof of Theorem 3o3cs
StepHypRef Expression
1 df-3or 935 . . 3  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ( ph  \/  ps )  \/  ch ) )
2 3o1cs.1 . . 3  |-  ( (
ph  \/  ps  \/  ch )  ->  th )
31, 2sylbir 204 . 2  |-  ( ( ( ph  \/  ps )  \/  ch )  ->  th )
43olcs 384 1  |-  ( ch 
->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 357    \/ w3o 933
This theorem is referenced by:  xrpxdivcld  23135
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359  df-3or 935
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