Theorem bj-2alim

Description: Closed form of 2alimi . (Contributed by BJ, 6-May-2019)

	Ref	Expression
Assertion	bj-2alim	⊢ ( ∀ 𝑥 ∀ 𝑦 ( 𝜑 → 𝜓 ) → ( ∀ 𝑥 ∀ 𝑦 𝜑 → ∀ 𝑥 ∀ 𝑦 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		alim	⊢ ( ∀ 𝑦 ( 𝜑 → 𝜓 ) → ( ∀ 𝑦 𝜑 → ∀ 𝑦 𝜓 ) )
2	1	al2imi	⊢ ( ∀ 𝑥 ∀ 𝑦 ( 𝜑 → 𝜓 ) → ( ∀ 𝑥 ∀ 𝑦 𝜑 → ∀ 𝑥 ∀ 𝑦 𝜓 ) )