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Theorem 3ori 1242
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 476 . 2  |-  ( -.  ( ph  \/  ps ) 
<->  ( -.  ph  /\  -.  ps ) )
2 3ori.1 . . . 4  |-  ( ph  \/  ps  \/  ch )
3 df-3or 935 . . . 4  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ( ph  \/  ps )  \/  ch ) )
42, 3mpbi 199 . . 3  |-  ( (
ph  \/  ps )  \/  ch )
54ori 364 . 2  |-  ( -.  ( ph  \/  ps )  ->  ch )
61, 5sylbir 204 1  |-  ( ( -.  ph  /\  -.  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 357    /\ wa 358    \/ w3o 933
This theorem is referenced by:  rankxplim3  7551
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-an 360  df-3or 935
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