Theorem bj-hbex

Description: A more general instance of hbex . (Contributed by BJ, 4-Apr-2026)

	Ref	Expression
Hypothesis	bj-hbex.1	$$⊢\phi \to \forall x\psi$$
Assertion	bj-hbex	$$⊢\exists y\phi \to \forall x\exists y\psi$$

Proof

Step	Hyp	Ref	Expression
1		bj-hbex.1	$$⊢\phi \to \forall x\psi$$
2		19.12	$$⊢\exists y\forall x\psi \to \forall x\exists y\psi$$
3	2 1	bj-sylge	$$⊢\exists y\phi \to \forall x\exists y\psi$$