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Theorem 3jaodan 1238
Description: Disjunction of 3 antecedents (deduction). (Contributed by NM, 14-Oct-2005.)
Hypotheses
Ref Expression
3jaodan.1  |-  ( (
ph  /\  ps )  ->  ch )
3jaodan.2  |-  ( (
ph  /\  th )  ->  ch )
3jaodan.3  |-  ( (
ph  /\  ta )  ->  ch )
Assertion
Ref Expression
3jaodan  |-  ( (
ph  /\  ( ps  \/  th  \/  ta )
)  ->  ch )

Proof of Theorem 3jaodan
StepHypRef Expression
1 3jaodan.1 . . . 4  |-  ( (
ph  /\  ps )  ->  ch )
21ex 113 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 3jaodan.2 . . . 4  |-  ( (
ph  /\  th )  ->  ch )
43ex 113 . . 3  |-  ( ph  ->  ( th  ->  ch ) )
5 3jaodan.3 . . . 4  |-  ( (
ph  /\  ta )  ->  ch )
65ex 113 . . 3  |-  ( ph  ->  ( ta  ->  ch ) )
72, 4, 63jaod 1236 . 2  |-  ( ph  ->  ( ( ps  \/  th  \/  ta )  ->  ch ) )
87imp 122 1  |-  ( (
ph  /\  ( ps  \/  th  \/  ta )
)  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    \/ w3o 919
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663
This theorem depends on definitions:  df-bi 115  df-3or 921  df-3an 922
This theorem is referenced by:  zeo  8533  xrltnsym  8944  xrlttr  8946  xrltso  8947  xrlttri3  8948  xltnegi  8978  qbtwnxr  9344
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