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Metamath Proof Explorer

Theorem syldan

Description: A syllogism deduction with conjoined antecedents. (Contributed by NM, 24-Feb-2005) (Proof shortened by Wolf Lammen, 6-Apr-2013)

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

Proof

Step Hyp Ref Expression
1 syldan.1 ⊢ φ ∧ ψ → χ
2 syldan.2 ⊢ φ ∧ χ → θ
3 simpl ⊢ φ ∧ ψ → φ
4 3 1 2 syl2anc ⊢ φ ∧ ψ → θ