This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

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 )