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Theorem 3ori 1300
Description: Infer implication from triple disjunction. (Contributed by NM, 26-Sep-2006.)
Hypothesis
Ref Expression
3ori.1  |-  ( ph  \/  ps  \/  ch )
Assertion
Ref Expression
3ori  |-  ( ( -.  ph  /\  -.  ps )  ->  ch )

Proof of Theorem 3ori
StepHypRef Expression
1 ioran 752 . 2  |-  ( -.  ( ph  \/  ps ) 
<->  ( -.  ph  /\  -.  ps ) )
2 3ori.1 . . . 4  |-  ( ph  \/  ps  \/  ch )
3 df-3or 979 . . . 4  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ( ph  \/  ps )  \/  ch ) )
42, 3mpbi 145 . . 3  |-  ( (
ph  \/  ps )  \/  ch )
54ori 723 . 2  |-  ( -.  ( ph  \/  ps )  ->  ch )
61, 5sylbir 135 1  |-  ( ( -.  ph  /\  -.  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 104    \/ wo 708    \/ w3o 977
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709
This theorem depends on definitions:  df-bi 117  df-3or 979
This theorem is referenced by: (None)
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