Theorem bj-2exbi

Description: Closed form of 2exbii . (Contributed by BJ, 6-May-2019)

	Ref	Expression
Assertion	bj-2exbi	⊢ ( ∀ 𝑥 ∀ 𝑦 ( 𝜑 ↔ 𝜓 ) → ( ∃ 𝑥 ∃ 𝑦 𝜑 ↔ ∃ 𝑥 ∃ 𝑦 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		exbi	⊢ ( ∀ 𝑦 ( 𝜑 ↔ 𝜓 ) → ( ∃ 𝑦 𝜑 ↔ ∃ 𝑦 𝜓 ) )
2	1	alexbii	⊢ ( ∀ 𝑥 ∀ 𝑦 ( 𝜑 ↔ 𝜓 ) → ( ∃ 𝑥 ∃ 𝑦 𝜑 ↔ ∃ 𝑥 ∃ 𝑦 𝜓 ) )