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Theorem ecase 933
Description: Inference for elimination by cases. (Contributed by NM, 13-Jul-2005.)
Hypotheses
Ref Expression
ecase.1  |-  ( -. 
ph  ->  ch )
ecase.2  |-  ( -. 
ps  ->  ch )
ecase.3  |-  ( (
ph  /\  ps )  ->  ch )
Assertion
Ref Expression
ecase  |-  ch

Proof of Theorem ecase
StepHypRef Expression
1 ecase.3 . . 3  |-  ( (
ph  /\  ps )  ->  ch )
21ex 434 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
3 ecase.1 . 2  |-  ( -. 
ph  ->  ch )
4 ecase.2 . 2  |-  ( -. 
ps  ->  ch )
52, 3, 4pm2.61nii 166 1  |-  ch
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by:  elfiun  7685  hashprb  12162  txindislem  19211  1to3vfriswmgra  30604
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