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Theorem jaoa 640
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 264 . 2  |-  ( ph  ->  ( ( ps  /\  ta )  ->  ch )
)
3 jaao.2 . . 3  |-  ( th 
->  ( ta  ->  ch ) )
43adantld 263 . 2  |-  ( th 
->  ( ( ps  /\  ta )  ->  ch )
)
52, 4jaoi 636 1  |-  ( (
ph  \/  th )  ->  ( ( ps  /\  ta )  ->  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 97    \/ wo 629
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm4.79dc  809
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