Theorem bj-alimdh

Description: General instance of alimdh . (Contributed by NM, 4-Jan-2002) State the most general derivable instance. (Revised by BJ, 5-Apr-2026)

	Ref	Expression
Hypotheses	bj-alimdh.nf	$$⊢\phi \to \forall x\psi$$
	bj-alimdh.maj	$$⊢\psi \to \left(\chi \to \theta \right)$$
Assertion	bj-alimdh	$$⊢\phi \to \left(\forall x\chi \to \forall x\theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		bj-alimdh.nf	$$⊢\phi \to \forall x\psi$$
2		bj-alimdh.maj	$$⊢\psi \to \left(\chi \to \theta \right)$$
3	2	al2imi	$$⊢\forall x\psi \to \left(\forall x\chi \to \forall x\theta \right)$$
4	1 3	syl	$$⊢\phi \to \left(\forall x\chi \to \forall x\theta \right)$$