Theorem 2alim

Description: Theorem *11.32 in WhiteheadRussell p. 162. Theorem 19.20 of Margaris p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011)

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

Proof

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