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Theorem ccase 937
Description: Inference for combining cases. (Contributed by NM, 29-Jul-1999.) (Proof shortened by Wolf Lammen, 6-Jan-2013.)
Hypotheses
Ref Expression
ccase.1  |-  ( (
ph  /\  ps )  ->  ta )
ccase.2  |-  ( ( ch  /\  ps )  ->  ta )
ccase.3  |-  ( (
ph  /\  th )  ->  ta )
ccase.4  |-  ( ( ch  /\  th )  ->  ta )
Assertion
Ref Expression
ccase  |-  ( ( ( ph  \/  ch )  /\  ( ps  \/  th ) )  ->  ta )

Proof of Theorem ccase
StepHypRef Expression
1 ccase.1 . . 3  |-  ( (
ph  /\  ps )  ->  ta )
2 ccase.2 . . 3  |-  ( ( ch  /\  ps )  ->  ta )
31, 2jaoian 782 . 2  |-  ( ( ( ph  \/  ch )  /\  ps )  ->  ta )
4 ccase.3 . . 3  |-  ( (
ph  /\  th )  ->  ta )
5 ccase.4 . . 3  |-  ( ( ch  /\  th )  ->  ta )
64, 5jaoian 782 . 2  |-  ( ( ( ph  \/  ch )  /\  th )  ->  ta )
73, 6jaodan 783 1  |-  ( ( ( ph  \/  ch )  /\  ( ps  \/  th ) )  ->  ta )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ wo 368    /\ 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-or 370  df-an 371
This theorem is referenced by:  ccased  938  ccase2  939  undif3  3610  injresinjlem  11637  hash2prd  12180  nn0gcdsq  13829  symgextf1  15925  cnmsgnsubg  18006  prodmo  27448  kelac2lem  29415
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