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Theorem 3jaoian 1250
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 425 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 3jaoian.2 . . . 4  |-  ( ( th  /\  ps )  ->  ch )
43ex 425 . . 3  |-  ( th 
->  ( ps  ->  ch ) )
5 3jaoian.3 . . . 4  |-  ( ( ta  /\  ps )  ->  ch )
65ex 425 . . 3  |-  ( ta 
->  ( ps  ->  ch ) )
72, 4, 63jaoi 1248 . 2  |-  ( (
ph  \/  th  \/  ta )  ->  ( ps  ->  ch ) )
87imp 420 1  |-  ( ( ( ph  \/  th  \/  ta )  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360    \/ w3o 936
This theorem is referenced by:  xrltnsym  10761  xrlttri  10763  xrlttr  10764  qbtwnxr  10817  xltnegi  10833  xaddcom  10855  xnegdi  10858  xaddeq0  24150  3ccased  25207
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 179  df-or 361  df-an 362  df-3or 938  df-3an 939
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