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Theorem jaao 709
Description: Inference conjoining and disjoining the antecedents of two implications. (Contributed by NM, 30-Sep-1999.)
Hypotheses
Ref Expression
jaao.1  |-  ( ph  ->  ( ps  ->  ch ) )
jaao.2  |-  ( th 
->  ( ta  ->  ch ) )
Assertion
Ref Expression
jaao  |-  ( (
ph  /\  th )  ->  ( ( ps  \/  ta )  ->  ch )
)

Proof of Theorem jaao
StepHypRef Expression
1 jaao.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21adantr 274 . 2  |-  ( (
ph  /\  th )  ->  ( ps  ->  ch ) )
3 jaao.2 . . 3  |-  ( th 
->  ( ta  ->  ch ) )
43adantl 275 . 2  |-  ( (
ph  /\  th )  ->  ( ta  ->  ch ) )
52, 4jaod 707 1  |-  ( (
ph  /\  th )  ->  ( ( ps  \/  ta )  ->  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    \/ wo 698
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  pm3.48  775  prlem1  958  nford  1547  funun  5214  poxp  6179  nntri3or  6440
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