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Theorem sylancbr 416
Description: A syllogism inference combined with contraction. (Contributed by NM, 3-Sep-2004.)
Hypotheses
Ref Expression
sylancbr.1  |-  ( ps  <->  ph )
sylancbr.2  |-  ( ch  <->  ph )
sylancbr.3  |-  ( ( ps  /\  ch )  ->  th )
Assertion
Ref Expression
sylancbr  |-  ( ph  ->  th )

Proof of Theorem sylancbr
StepHypRef Expression
1 sylancbr.1 . . 3  |-  ( ps  <->  ph )
2 sylancbr.2 . . 3  |-  ( ch  <->  ph )
3 sylancbr.3 . . 3  |-  ( ( ps  /\  ch )  ->  th )
41, 2, 3syl2anbr 290 . 2  |-  ( (
ph  /\  ph )  ->  th )
54anidms 395 1  |-  ( ph  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    <-> wb 104
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
This theorem is referenced by: (None)
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