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Theorem 3ori 1206
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 679 . 2  |-  ( -.  ( ph  \/  ps ) 
<->  ( -.  ph  /\  -.  ps ) )
2 3ori.1 . . . 4  |-  ( ph  \/  ps  \/  ch )
3 df-3or 897 . . . 4  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ( ph  \/  ps )  \/  ch ) )
42, 3mpbi 137 . . 3  |-  ( (
ph  \/  ps )  \/  ch )
54ori 652 . 2  |-  ( -.  ( ph  \/  ps )  ->  ch )
61, 5sylbir 129 1  |-  ( ( -.  ph  /\  -.  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 101    \/ wo 639    \/ w3o 895
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640
This theorem depends on definitions:  df-bi 114  df-3or 897
This theorem is referenced by: (None)
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