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Theorem sylanblrc 413
Description: Syllogism inference combined with a biconditional. (Contributed by BJ, 25-Apr-2019.)
Hypotheses
Ref Expression
sylanblrc.1  |-  ( ph  ->  ps )
sylanblrc.2  |-  ch
sylanblrc.3  |-  ( th  <->  ( ps  /\  ch )
)
Assertion
Ref Expression
sylanblrc  |-  ( ph  ->  th )

Proof of Theorem sylanblrc
StepHypRef Expression
1 sylanblrc.1 . 2  |-  ( ph  ->  ps )
2 sylanblrc.2 . 2  |-  ch
3 sylanblrc.3 . . 3  |-  ( th  <->  ( ps  /\  ch )
)
43biimpri 132 . 2  |-  ( ( ps  /\  ch )  ->  th )
51, 2, 4sylancl 410 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:  cosmul  11486  cdivcncfap  12793  dvrecap  12883
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