Theorem 2al2imi

Description: Removes two universal quantifiers from a statement. (Contributed by Andrew Salmon, 24-May-2011)

	Ref	Expression
Hypothesis	2al2imi.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	2al2imi	⊢ ( ∀ 𝑥 ∀ 𝑦 𝜑 → ( ∀ 𝑥 ∀ 𝑦 𝜓 → ∀ 𝑥 ∀ 𝑦 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		2al2imi.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2	1	al2imi	⊢ ( ∀ 𝑦 𝜑 → ( ∀ 𝑦 𝜓 → ∀ 𝑦 𝜒 ) )
3	2	al2imi	⊢ ( ∀ 𝑥 ∀ 𝑦 𝜑 → ( ∀ 𝑥 ∀ 𝑦 𝜓 → ∀ 𝑥 ∀ 𝑦 𝜒 ) )