Theorem 2alimi

Description: Inference doubly quantifying both antecedent and consequent. (Contributed by NM, 3-Feb-2005)

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

Proof

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