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	⊢ ∀ 𝑥 ( 𝜓 → 𝜑 )
	bj-almp.min	⊢ ∀ 𝑥 𝜓
Assertion	bj-almp	⊢ ∀ 𝑥 𝜑

Proof

Step	Hyp	Ref	Expression
1		bj-almp.maj	⊢ ∀ 𝑥 ( 𝜓 → 𝜑 )
2		bj-almp.min	⊢ ∀ 𝑥 𝜓
3		alim	⊢ ( ∀ 𝑥 ( 𝜓 → 𝜑 ) → ( ∀ 𝑥 𝜓 → ∀ 𝑥 𝜑 ) )
4	1 2 3	mp2	⊢ ∀ 𝑥 𝜑