Theorem bj-hbald

Description: General statement that hbald proves . (Contributed by BJ, 4-Apr-2026)

	Ref	Expression
Hypotheses	bj-hbald.1	$$⊢\phi \to \forall y\psi$$
	bj-hbald.2	$$⊢\psi \to \left(\chi \to \forall x\theta \right)$$
Assertion	bj-hbald	$$⊢\phi \to \left(\forall y\chi \to \forall x\forall y\theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		bj-hbald.1	$$⊢\phi \to \forall y\psi$$
2		bj-hbald.2	$$⊢\psi \to \left(\chi \to \forall x\theta \right)$$
3	2	al2imi	$$⊢\forall y\psi \to \left(\forall y\chi \to \forall y\forall x\theta \right)$$
4	1 3	syl	$$⊢\phi \to \left(\forall y\chi \to \forall y\forall x\theta \right)$$
5		ax-11	$$⊢\forall y\forall x\theta \to \forall x\forall y\theta$$
6	4 5	syl6	$$⊢\phi \to \left(\forall y\chi \to \forall x\forall y\theta \right)$$