Theorem 3albii

Description: Inference adding three universal quantifiers to both sides of an equivalence. (Contributed by Peter Mazsa, 10-Aug-2018)

	Ref	Expression
Hypothesis	albii.1	⊢ ( 𝜑 ↔ 𝜓 )
Assertion	3albii	⊢ ( ∀ 𝑥 ∀ 𝑦 ∀ 𝑧 𝜑 ↔ ∀ 𝑥 ∀ 𝑦 ∀ 𝑧 𝜓 )

Proof

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