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Metamath Proof Explorer

Theorem syl3anr1

Description: A syllogism inference. (Contributed by NM, 31-Jul-2007)

Ref Expression
Hypotheses syl3anr1.1 ⊢ φ → ψ
syl3anr1.2 ⊢ χ ∧ ψ ∧ θ ∧ τ → η
Assertion syl3anr1 ⊢ χ ∧ φ ∧ θ ∧ τ → η

Proof

Step Hyp Ref Expression
1 syl3anr1.1 ⊢ φ → ψ
2 syl3anr1.2 ⊢ χ ∧ ψ ∧ θ ∧ τ → η
3 1 3anim1i ⊢ φ ∧ θ ∧ τ → ψ ∧ θ ∧ τ
4 3 2 sylan2 ⊢ χ ∧ φ ∧ θ ∧ τ → η