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Theorem ccase2 914
Description: Inference for combining cases. (Contributed by NM, 29-Jul-1999.)
Hypotheses
Ref Expression
ccase2.1  |-  ( (
ph  /\  ps )  ->  ta )
ccase2.2  |-  ( ch 
->  ta )
ccase2.3  |-  ( th 
->  ta )
Assertion
Ref Expression
ccase2  |-  ( ( ( ph  \/  ch )  /\  ( ps  \/  th ) )  ->  ta )

Proof of Theorem ccase2
StepHypRef Expression
1 ccase2.1 . 2  |-  ( (
ph  /\  ps )  ->  ta )
2 ccase2.2 . . 3  |-  ( ch 
->  ta )
32adantr 451 . 2  |-  ( ( ch  /\  ps )  ->  ta )
4 ccase2.3 . . 3  |-  ( th 
->  ta )
54adantl 452 . 2  |-  ( (
ph  /\  th )  ->  ta )
64adantl 452 . 2  |-  ( ( ch  /\  th )  ->  ta )
71, 3, 5, 6ccase 912 1  |-  ( ( ( ph  \/  ch )  /\  ( ps  \/  th ) )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 357    /\ wa 358
This theorem is referenced by:  fctop  16741  cctop  16743
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
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