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Theorem 3jaoian 1247
Description: Disjunction of 3 antecedents (inference). (Contributed by NM, 14-Oct-2005.)
Hypotheses
Ref Expression
3jaoian.1  |-  ( (
ph  /\  ps )  ->  ch )
3jaoian.2  |-  ( ( th  /\  ps )  ->  ch )
3jaoian.3  |-  ( ( ta  /\  ps )  ->  ch )
Assertion
Ref Expression
3jaoian  |-  ( ( ( ph  \/  th  \/  ta )  /\  ps )  ->  ch )

Proof of Theorem 3jaoian
StepHypRef Expression
1 3jaoian.1 . . . 4  |-  ( (
ph  /\  ps )  ->  ch )
21ex 423 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 3jaoian.2 . . . 4  |-  ( ( th  /\  ps )  ->  ch )
43ex 423 . . 3  |-  ( th 
->  ( ps  ->  ch ) )
5 3jaoian.3 . . . 4  |-  ( ( ta  /\  ps )  ->  ch )
65ex 423 . . 3  |-  ( ta 
->  ( ps  ->  ch ) )
72, 4, 63jaoi 1245 . 2  |-  ( (
ph  \/  th  \/  ta )  ->  ( ps  ->  ch ) )
87imp 418 1  |-  ( ( ( ph  \/  th  \/  ta )  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    \/ w3o 933
This theorem is referenced by:  xrltnsym  10487  xrlttri  10489  xrlttr  10490  qbtwnxr  10543  xltnegi  10559  xaddcom  10581  xnegdi  10584  xaddeq0  23319  3ccased  24088
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  df-3an 936
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