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Metamath Proof Explorer

Theorem syl3anr3

Description: A syllogism inference. (Contributed by NM, 23-Aug-2007)

Ref Expression
Hypotheses syl3anr3.1 ⊢ φ → τ
syl3anr3.2 ⊢ χ ∧ ψ ∧ θ ∧ τ → η
Assertion syl3anr3 ⊢ χ ∧ ψ ∧ θ ∧ φ → η

Proof

Step Hyp Ref Expression
1 syl3anr3.1 ⊢ φ → τ
2 syl3anr3.2 ⊢ χ ∧ ψ ∧ θ ∧ τ → η
3 1 3anim3i ⊢ ψ ∧ θ ∧ φ → ψ ∧ θ ∧ τ
4 3 2 sylan2 ⊢ χ ∧ ψ ∧ θ ∧ φ → η