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Theorem ecase3 907
Description: Inference for elimination by cases. (Contributed by NM, 23-Mar-1995.) (Proof shortened by Wolf Lammen, 26-Nov-2012.)
Hypotheses
Ref Expression
ecase3.1  |-  ( ph  ->  ch )
ecase3.2  |-  ( ps 
->  ch )
ecase3.3  |-  ( -.  ( ph  \/  ps )  ->  ch )
Assertion
Ref Expression
ecase3  |-  ch

Proof of Theorem ecase3
StepHypRef Expression
1 ecase3.1 . . 3  |-  ( ph  ->  ch )
2 ecase3.2 . . 3  |-  ( ps 
->  ch )
31, 2jaoi 368 . 2  |-  ( (
ph  \/  ps )  ->  ch )
4 ecase3.3 . 2  |-  ( -.  ( ph  \/  ps )  ->  ch )
53, 4pm2.61i 156 1  |-  ch
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 357
This theorem is referenced by:  equvini  1927  eueq3  2940  mdsymi  22991
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
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