Theorem 2exbii

Description: Inference adding two existential quantifiers to both sides of an equivalence. (Contributed by NM, 16-Mar-1995)

	Ref	Expression
Hypothesis	2exbii.1	⊢ ( 𝜑 ↔ 𝜓 )
Assertion	2exbii	⊢ ( ∃ 𝑥 ∃ 𝑦 𝜑 ↔ ∃ 𝑥 ∃ 𝑦 𝜓 )

Proof

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