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Theorem syl3an3b 1276
Description: A syllogism inference. (Contributed by NM, 22-Aug-1995.)
Hypotheses
Ref Expression
syl3an3b.1  |-  ( ph  <->  th )
syl3an3b.2  |-  ( ( ps  /\  ch  /\  th )  ->  ta )
Assertion
Ref Expression
syl3an3b  |-  ( ( ps  /\  ch  /\  ph )  ->  ta )

Proof of Theorem syl3an3b
StepHypRef Expression
1 syl3an3b.1 . . 3  |-  ( ph  <->  th )
21biimpi 120 . 2  |-  ( ph  ->  th )
3 syl3an3b.2 . 2  |-  ( ( ps  /\  ch  /\  th )  ->  ta )
42, 3syl3an3 1273 1  |-  ( ( ps  /\  ch  /\  ph )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 105    /\ w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 980
This theorem is referenced by:  fvun2  5578  nnmsucr  6482  apreim  8537  xrlttr  9769  xrltso  9770  iccdil  9972  icccntr  9974  absexpzap  11060  unicld  13249
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