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Theorem sylbb1 135
Description: A mixed syllogism inference from two biconditionals. (Contributed by BJ, 21-Apr-2019.)
Hypotheses
Ref Expression
sylbb1.1  |-  ( ph  <->  ps )
sylbb1.2  |-  ( ph  <->  ch )
Assertion
Ref Expression
sylbb1  |-  ( ps 
->  ch )

Proof of Theorem sylbb1
StepHypRef Expression
1 sylbb1.1 . . 3  |-  ( ph  <->  ps )
21biimpri 131 . 2  |-  ( ps 
->  ph )
3 sylbb1.2 . 2  |-  ( ph  <->  ch )
42, 3sylib 120 1  |-  ( ps 
->  ch )
Colors of variables: wff set class
Syntax hints:    -> 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
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  expival  9611
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