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Theorem syl3an3br 1240
Description: A syllogism inference. (Contributed by NM, 22-Aug-1995.)
Hypotheses
Ref Expression
syl3an3br.1  |-  ( th  <->  ph )
syl3an3br.2  |-  ( ( ps  /\  ch  /\  th )  ->  ta )
Assertion
Ref Expression
syl3an3br  |-  ( ( ps  /\  ch  /\  ph )  ->  ta )

Proof of Theorem syl3an3br
StepHypRef Expression
1 syl3an3br.1 . . 3  |-  ( th  <->  ph )
21biimpri 132 . 2  |-  ( ph  ->  th )
3 syl3an3br.2 . 2  |-  ( ( ps  /\  ch  /\  th )  ->  ta )
42, 3syl3an3 1234 1  |-  ( ( ps  /\  ch  /\  ph )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104    /\ w3a 945
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 947
This theorem is referenced by:  opelrng  4739  phpeqd  6787
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