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	⊢ ( ∃ 𝑥 𝜑 → ( ∀ 𝑥 𝜓 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		bj-axdd2	⊢ ( ∃ 𝑥 𝜑 → ( ∀ 𝑥 𝜓 → ∃ 𝑥 𝜓 ) )
2		ax5e	⊢ ( ∃ 𝑥 𝜓 → 𝜓 )
3	1 2	syl6	⊢ ( ∃ 𝑥 𝜑 → ( ∀ 𝑥 𝜓 → 𝜓 ) )