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Theorem jaoa 496
Description: Inference disjoining and conjoining the antecedents of two implications. (Contributed by Stefan Allan, 1-Nov-2008.)
Hypotheses
Ref Expression
jaao.1  |-  ( ph  ->  ( ps  ->  ch ) )
jaao.2  |-  ( th 
->  ( ta  ->  ch ) )
Assertion
Ref Expression
jaoa  |-  ( (
ph  \/  th )  ->  ( ( ps  /\  ta )  ->  ch )
)

Proof of Theorem jaoa
StepHypRef Expression
1 jaao.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21adantrd 454 . 2  |-  ( ph  ->  ( ( ps  /\  ta )  ->  ch )
)
3 jaao.2 . . 3  |-  ( th 
->  ( ta  ->  ch ) )
43adantld 453 . 2  |-  ( th 
->  ( ( ps  /\  ta )  ->  ch )
)
52, 4jaoi 368 1  |-  ( (
ph  \/  th )  ->  ( ( ps  /\  ta )  ->  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 357    /\ wa 358
This theorem is referenced by:  pm4.79  566  abslt  11798  absle  11799  uncon  17155  dfon2lem4  24142
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
  Copyright terms: Public domain W3C validator