Theorem bj-almp

Description: A quantified form of ax-mp . See also barbara , bj-almpi , and the inference associated with ala1 . (Contributed by BJ, 19-Mar-2026) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	bj-almp.maj	$$⊢\forall x\left(\psi \to \phi \right)$$
	bj-almp.min	$$⊢\forall x\psi$$
Assertion	bj-almp	$$⊢\forall x\phi$$

Proof

Step	Hyp	Ref	Expression
1		bj-almp.maj	$$⊢\forall x\left(\psi \to \phi \right)$$
2		bj-almp.min	$$⊢\forall x\psi$$
3		alim	$$⊢\forall x\left(\psi \to \phi \right)\to \left(\forall x\psi \to \forall x\phi \right)$$
4	1 2 3	mp2	$$⊢\forall x\phi$$