Metamath Proof Explorer


Theorem spsv

Description: Generalization of antecedent. A trivial weak version of sps avoiding ax-12 . (Contributed by SN, 13-Nov-2025) (Proof shortened by WL, 19-Nov-2025)

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

Proof

Step Hyp Ref Expression
1 spsv.1 ⊢ φ → ψ
2 1 a1i ⊢ x = y → φ → ψ
3 2 spimvw ⊢ ∀ x φ → ψ