Theorem 2alanimi

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

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

Proof

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