Theorem bj-alimdh 36856

Description: General instance of alimdh 1819. (Contributed by NM, 4-Jan-2002.) State the most general derivable instance. (Revised by BJ, 5-Apr-2026.)

Hypotheses

Ref	Expression
bj-alimdh.nf	⊢ (𝜑 → ∀𝑥𝜓)
bj-alimdh.maj	⊢ (𝜓 → (𝜒 → 𝜃))

Assertion

Ref	Expression
bj-alimdh	⊢ (𝜑 → (∀𝑥𝜒 → ∀𝑥𝜃))

Proof of Theorem bj-alimdh

Step	Hyp	Ref	Expression
1		bj-alimdh.nf	. 2 ⊢ (𝜑 → ∀𝑥𝜓)
2		bj-alimdh.maj	. . 3 ⊢ (𝜓 → (𝜒 → 𝜃))
3	2	al2imi 1817	. 2 ⊢ (∀𝑥𝜓 → (∀𝑥𝜒 → ∀𝑥𝜃))
4	1, 3	syl 17	1 ⊢ (𝜑 → (∀𝑥𝜒 → ∀𝑥𝜃))

Syntax hints:   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1797  ax-4 1811

This theorem is referenced by:  bj-alrimdh  36857