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Metamath Proof Explorer

Theorem syl6ci

Description: A syllogism inference combined with contraction. (Contributed by Alan Sare, 18-Mar-2012)

Ref Expression
Hypotheses syl6ci.1 ⊢ φ → ψ → χ
syl6ci.2 ⊢ φ → θ
syl6ci.3 ⊢ χ → θ → τ
Assertion syl6ci ⊢ φ → ψ → τ

Proof

Step Hyp Ref Expression
1 syl6ci.1 ⊢ φ → ψ → χ
2 syl6ci.2 ⊢ φ → θ
3 syl6ci.3 ⊢ χ → θ → τ
4 2 a1d ⊢ φ → ψ → θ
5 1 4 3 syl6c ⊢ φ → ψ → τ