Theorem 2moex

Description: Double quantification with "at most one". Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker 2moexv when possible. (Contributed by NM, 3-Dec-2001) (New usage is discouraged.)

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

Proof

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