Theorem 2albii

Description: Inference adding two universal quantifiers to both sides of an equivalence. (Contributed by NM, 9-Mar-1997)

	Ref	Expression
Hypothesis	albii.1	⊢ ( 𝜑 ↔ 𝜓 )
Assertion	2albii	⊢ ( ∀ 𝑥 ∀ 𝑦 𝜑 ↔ ∀ 𝑥 ∀ 𝑦 𝜓 )

Proof

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