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Theorem sylanblc 411
Description: Syllogism inference combined with a biconditional. (Contributed by BJ, 25-Apr-2019.)
Hypotheses
Ref Expression
sylanblc.1  |-  ( ph  ->  ps )
sylanblc.2  |-  ch
sylanblc.3  |-  ( ( ps  /\  ch )  <->  th )
Assertion
Ref Expression
sylanblc  |-  ( ph  ->  th )

Proof of Theorem sylanblc
StepHypRef Expression
1 sylanblc.1 . 2  |-  ( ph  ->  ps )
2 sylanblc.2 . 2  |-  ch
3 sylanblc.3 . . 3  |-  ( ( ps  /\  ch )  <->  th )
43biimpi 119 . 2  |-  ( ( ps  /\  ch )  ->  th )
51, 2, 4sylancl 409 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-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by: (None)
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