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	$$⊢\phi \to \psi$$
Assertion	spsv	$$⊢\forall x\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		spsv.1	$$⊢\phi \to \psi$$
2	1	a1i	$$⊢x=y\to \left(\phi \to \psi \right)$$
3	2	spimvw	$$⊢\forall x\phi \to \psi$$