Theorem 2moexv

Description: Double quantification with "at most one". (Contributed by NM, 3-Dec-2001)

	Ref	Expression
Assertion	2moexv	⊢ ( ∃* 𝑥 ∃ 𝑦 𝜑 → ∀ 𝑦 ∃* 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		nfe1	⊢ Ⅎ 𝑦 ∃ 𝑦 𝜑
2	1	nfmov	⊢ Ⅎ 𝑦 ∃* 𝑥 ∃ 𝑦 𝜑
3		19.8a	⊢ ( 𝜑 → ∃ 𝑦 𝜑 )
4	3	moimi	⊢ ( ∃* 𝑥 ∃ 𝑦 𝜑 → ∃* 𝑥 𝜑 )
5	2 4	alrimi	⊢ ( ∃* 𝑥 ∃ 𝑦 𝜑 → ∀ 𝑦 ∃* 𝑥 𝜑 )