Theorem bj-hbalt

Description: Closed form of (general instance of) hbal . (Contributed by BJ, 2-May-2019)

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

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\forall y\left(\phi \to \forall x\psi \right)\to \forall y\left(\phi \to \forall x\psi \right)$$
2		id	$$⊢\left(\phi \to \forall x\psi \right)\to \left(\phi \to \forall x\psi \right)$$
3	1 2	bj-hbald	$$⊢\forall y\left(\phi \to \forall x\psi \right)\to \left(\forall y\phi \to \forall x\forall y\psi \right)$$