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Theorem sylnbir 637
Description: A mixed syllogism inference from a biconditional and an implication. (Contributed by Wolf Lammen, 16-Dec-2013.)
Hypotheses
Ref Expression
sylnbir.1  |-  ( ps  <->  ph )
sylnbir.2  |-  ( -. 
ps  ->  ch )
Assertion
Ref Expression
sylnbir  |-  ( -. 
ph  ->  ch )

Proof of Theorem sylnbir
StepHypRef Expression
1 sylnbir.1 . . 3  |-  ( ps  <->  ph )
21bicomi 130 . 2  |-  ( ph  <->  ps )
3 sylnbir.2 . 2  |-  ( -. 
ps  ->  ch )
42, 3sylnbi 636 1  |-  ( -. 
ph  ->  ch )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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