Theorem 2alimdv

Description: Deduction form of Theorem 19.20 of Margaris p. 90 with two quantifiers, see alim . (Contributed by NM, 27-Apr-2004)

	Ref	Expression
Hypothesis	2alimdv.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	2alimdv	⊢ ( 𝜑 → ( ∀ 𝑥 ∀ 𝑦 𝜓 → ∀ 𝑥 ∀ 𝑦 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		2alimdv.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2	1	alimdv	⊢ ( 𝜑 → ( ∀ 𝑦 𝜓 → ∀ 𝑦 𝜒 ) )
3	2	alimdv	⊢ ( 𝜑 → ( ∀ 𝑥 ∀ 𝑦 𝜓 → ∀ 𝑥 ∀ 𝑦 𝜒 ) )