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Metamath Proof Explorer

Theorem sylani

Description: A syllogism inference. (Contributed by NM, 2-May-1996)

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

Proof

Step Hyp Ref Expression
1 sylani.1 ⊢ φ → χ
2 sylani.2 ⊢ ψ → χ ∧ θ → τ
3 1 a1i ⊢ ψ → φ → χ
4 3 2 syland ⊢ ψ → φ ∧ θ → τ