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Metamath Proof Explorer

Theorem 3syl

Description: Inference chaining two syllogisms syl . Inference associated with imim12i . (Contributed by NM, 28-Dec-1992)

Ref Expression
Hypotheses 3syl.1 ⊢ φ → ψ
3syl.2 ⊢ ψ → χ
3syl.3 ⊢ χ → θ
Assertion 3syl ⊢ φ → θ

Proof

Step Hyp Ref Expression
1 3syl.1 ⊢ φ → ψ
2 3syl.2 ⊢ ψ → χ
3 3syl.3 ⊢ χ → θ
4 1 2 syl ⊢ φ → χ
5 4 3 syl ⊢ φ → θ