Theorem bj-spvw

Description: Version of spvw proved from ax-1 -- ax-5 and the existence axiom extru . (Contributed by BJ, 8-Mar-2026) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-spvw	$$⊢\exists x\phi \to \left(\forall x\psi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bj-axdd2	$$⊢\exists x\phi \to \left(\forall x\psi \to \exists x\psi \right)$$
2		ax5e	$$⊢\exists x\psi \to \psi$$
3	1 2	syl6	$$⊢\exists x\phi \to \left(\forall x\psi \to \psi \right)$$