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Metamath Proof Explorer

Theorem alsyl

Description: Universally quantified and uncurried (imported) form of syllogism. Theorem *10.3 in WhiteheadRussell p. 150. (Contributed by Andrew Salmon, 8-Jun-2011)

Ref Expression
Assertion alsyl ⊢ ∀ x φ → ψ ∧ ∀ x ψ → χ → ∀ x φ → χ

Proof

Step Hyp Ref Expression
1 pm3.33 ⊢ φ → ψ ∧ ψ → χ → φ → χ
2 1 alanimi ⊢ ∀ x φ → ψ ∧ ∀ x ψ → χ → ∀ x φ → χ