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Metamath Proof Explorer

Theorem syl3an1

Description: A syllogism inference. (Contributed by NM, 22-Aug-1995)

Ref Expression
Hypotheses syl3an1.1 ⊢ φ → ψ
syl3an1.2 ⊢ ψ ∧ χ ∧ θ → τ
Assertion syl3an1 ⊢ φ ∧ χ ∧ θ → τ

Proof

Step Hyp Ref Expression
1 syl3an1.1 ⊢ φ → ψ
2 syl3an1.2 ⊢ ψ ∧ χ ∧ θ → τ
3 1 3anim1i ⊢ φ ∧ χ ∧ θ → ψ ∧ χ ∧ θ
4 3 2 syl ⊢ φ ∧ χ ∧ θ → τ