Theorem 2moexv

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

	Ref	Expression
Assertion	2moexv	$$⊢{\exists }^{*}x\exists y\phi \to \forall y{\exists }^{*}x\phi$$

Proof

Step	Hyp	Ref	Expression
1		nfe1	$$⊢Ⅎy\exists y\phi$$
2	1	nfmov	$$⊢Ⅎy{\exists }^{*}x\exists y\phi$$
3		19.8a	$$⊢\phi \to \exists y\phi$$
4	3	moimi	$$⊢{\exists }^{*}x\exists y\phi \to {\exists }^{*}x\phi$$
5	2 4	alrimi	$$⊢{\exists }^{*}x\exists y\phi \to \forall y{\exists }^{*}x\phi$$