Metamath Proof Explorer


Theorem sps

Description: Generalization of antecedent. (Contributed by NM, 5-Jan-1993)

Ref Expression
Hypothesis sps.1 ⊢ φ → ψ
Assertion sps ⊢ ∀ x φ → ψ

Proof

Step Hyp Ref Expression
1 sps.1 ⊢ φ → ψ
2 sp ⊢ ∀ x φ → φ
3 2 1 syl ⊢ ∀ x φ → ψ