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Theorem sylanblrc 401
Description: Syllogism inference combined with a biconditional. (Contributed by BJ, 25-Apr-2019.)
Hypotheses
Ref Expression
sylanblrc.1 (𝜑𝜓)
sylanblrc.2 𝜒
sylanblrc.3 (𝜃 ↔ (𝜓𝜒))
Assertion
Ref Expression
sylanblrc (𝜑𝜃)

Proof of Theorem sylanblrc
StepHypRef Expression
1 sylanblrc.1 . 2 (𝜑𝜓)
2 sylanblrc.2 . 2 𝜒
3 sylanblrc.3 . . 3 (𝜃 ↔ (𝜓𝜒))
43biimpri 128 . 2 ((𝜓𝜒) → 𝜃)
51, 2, 4sylancl 398 1 (𝜑𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by: (None)
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