Theorem 2albidv

Description: Formula-building rule for two universal quantifiers (deduction form). (Contributed by NM, 4-Mar-1997)

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

Proof

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