Theorem bj-almpi

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

	Ref	Expression
Hypotheses	bj-almpi.maj	⊢ ∀ 𝑥 ( 𝜑 → ( 𝜒 → 𝜓 ) )
	bj-almpi.min	⊢ ∀ 𝑥 𝜒
Assertion	bj-almpi	⊢ ∀ 𝑥 ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		bj-almpi.maj	⊢ ∀ 𝑥 ( 𝜑 → ( 𝜒 → 𝜓 ) )
2		bj-almpi.min	⊢ ∀ 𝑥 𝜒
3		pm2.04	⊢ ( ( 𝜑 → ( 𝜒 → 𝜓 ) ) → ( 𝜒 → ( 𝜑 → 𝜓 ) ) )
4	3	alimi	⊢ ( ∀ 𝑥 ( 𝜑 → ( 𝜒 → 𝜓 ) ) → ∀ 𝑥 ( 𝜒 → ( 𝜑 → 𝜓 ) ) )
5	1 4	ax-mp	⊢ ∀ 𝑥 ( 𝜒 → ( 𝜑 → 𝜓 ) )
6	5 2	bj-almp	⊢ ∀ 𝑥 ( 𝜑 → 𝜓 )