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Theorem jaao 512
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 467 . 2  |-  ( (
ph  /\  th )  ->  ( ps  ->  ch ) )
3 jaao.2 . . 3  |-  ( th 
->  ( ta  ->  ch ) )
43adantl 468 . 2  |-  ( (
ph  /\  th )  ->  ( ta  ->  ch ) )
52, 4jaod 382 1  |-  ( (
ph  /\  th )  ->  ( ( ps  \/  ta )  ->  ch )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ wo 370    /\ wa 371
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 189  df-or 372  df-an 373
This theorem is referenced by:  pm3.44  514  pm3.48  844  prlem1  973  ordtri1  5456  ordun  5524  suc11  5526  funun  5624  poxp  6908  suc11reg  8124  rankunb  8321  gruun  9231  ofpreima2  28269  wl-orel12  31849
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