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Theorem syl3an3br 1223
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 197 . 2  |-  ( ph  ->  th )
3 syl3an3br.2 . 2  |-  ( ( ps  /\  ch  /\  th )  ->  ta )
42, 3syl3an3 1217 1  |-  ( ( ps  /\  ch  /\  ph )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ w3a 934
This theorem is referenced by:  ordintdif  4441  2ndcdisj2  17183  isosctrlem2  20119  endofsegid  24708  lsslinds  27301
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
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