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Theorem sylbb 122
Description: A mixed syllogism inference from two biconditionals. (Contributed by BJ, 30-Mar-2019.)
Hypotheses
Ref Expression
sylbb.1  |-  ( ph  <->  ps )
sylbb.2  |-  ( ps  <->  ch )
Assertion
Ref Expression
sylbb  |-  ( ph  ->  ch )

Proof of Theorem sylbb
StepHypRef Expression
1 sylbb.1 . 2  |-  ( ph  <->  ps )
2 sylbb.2 . . 3  |-  ( ps  <->  ch )
32biimpi 119 . 2  |-  ( ps 
->  ch )
41, 3sylbi 120 1  |-  ( ph  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  ctinfom  11948
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