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Theorem syl3an1b 1182
Description: A syllogism inference. (Contributed by NM, 22-Aug-1995.)
Hypotheses
Ref Expression
syl3an1b.1  |-  ( ph  <->  ps )
syl3an1b.2  |-  ( ( ps  /\  ch  /\  th )  ->  ta )
Assertion
Ref Expression
syl3an1b  |-  ( (
ph  /\  ch  /\  th )  ->  ta )

Proof of Theorem syl3an1b
StepHypRef Expression
1 syl3an1b.1 . . 3  |-  ( ph  <->  ps )
21biimpi 117 . 2  |-  ( ph  ->  ps )
3 syl3an1b.2 . 2  |-  ( ( ps  /\  ch  /\  th )  ->  ta )
42, 3syl3an1 1179 1  |-  ( (
ph  /\  ch  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 102    /\ w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  irrmul  8679  xrlttr  8817
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