Theorem bj-almpi 37411

Description: A quantified form of mpi 21. See also barbara 2687, bj-ala1i 37410, bj-almp 37403. (Contributed by BJ, 19-Mar-2026.)

Hypotheses

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

Assertion

Ref	Expression
bj-almpi	⊢ ∀𝑥(𝜑 → 𝜓)

Proof of Theorem bj-almpi

Step	Hyp	Ref	Expression
1		bj-almpi.maj	. . 3 ⊢ ∀𝑥(𝜑 → (𝜒 → 𝜓))
2		pm2.04 91	. . . 4 ⊢ ((𝜑 → (𝜒 → 𝜓)) → (𝜒 → (𝜑 → 𝜓)))
3	2	alimi 1844	. . 3 ⊢ (∀𝑥(𝜑 → (𝜒 → 𝜓)) → ∀𝑥(𝜒 → (𝜑 → 𝜓)))
4	1, 3	ax-mp 5	. 2 ⊢ ∀𝑥(𝜒 → (𝜑 → 𝜓))
5		bj-almpi.min	. 2 ⊢ ∀𝑥𝜒
6	4, 5	bj-almp 37403	1 ⊢ ∀𝑥(𝜑 → 𝜓)

This proof depends on syntax axioms:   → wi 4  ∀wal 1568

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1828  ax-4 1842

This theorem is used by:  bj-almpig  37412