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Theorem sylbb2 137
Description: A mixed syllogism inference from two biconditionals. (Contributed by BJ, 21-Apr-2019.)
Hypotheses
Ref Expression
sylbb2.1  |-  ( ph  <->  ps )
sylbb2.2  |-  ( ch  <->  ps )
Assertion
Ref Expression
sylbb2  |-  ( ph  ->  ch )

Proof of Theorem sylbb2
StepHypRef Expression
1 sylbb2.1 . 2  |-  ( ph  <->  ps )
2 sylbb2.2 . . 3  |-  ( ch  <->  ps )
32biimpri 132 . 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  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  inffiexmid  6766  ssfirab  6788  ctssexmid  6990  fsumsplitsnun  11128
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