Theorem bj-almpi

Description: A quantified form of mpi . See also barbara , bj-ala1i , bj-almp . (Contributed by BJ, 19-Mar-2026)

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

Proof

Step	Hyp	Ref	Expression
1		bj-almpi.maj	$$⊢\forall x\left(\phi \to \left(\chi \to \psi \right)\right)$$
2		bj-almpi.min	$$⊢\forall x\chi$$
3		pm2.04	$$⊢\left(\phi \to \left(\chi \to \psi \right)\right)\to \left(\chi \to \left(\phi \to \psi \right)\right)$$
4	3	alimi	$$⊢\forall x\left(\phi \to \left(\chi \to \psi \right)\right)\to \forall x\left(\chi \to \left(\phi \to \psi \right)\right)$$
5	1 4	ax-mp	$$⊢\forall x\left(\chi \to \left(\phi \to \psi \right)\right)$$
6	5 2	bj-almp	$$⊢\forall x\left(\phi \to \psi \right)$$