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Metamath Proof Explorer

Theorem sylanblrc

Description: Syllogism inference combined with a biconditional. (Contributed by BJ, 25-Apr-2019)

Ref Expression
Hypotheses sylanblrc.1 ⊢ φ → ψ
sylanblrc.2 ⊢ χ
sylanblrc.3 ⊢ θ ↔ ψ ∧ χ
Assertion sylanblrc ⊢ φ → θ

Proof

Step Hyp Ref Expression
1 sylanblrc.1 ⊢ φ → ψ
2 sylanblrc.2 ⊢ χ
3 sylanblrc.3 ⊢ θ ↔ ψ ∧ χ
4 2 a1i ⊢ φ → χ
5 1 4 3 sylanbrc ⊢ φ → θ