Theorem 2eumo

Description: Nested unique existential quantifier and at-most-one quantifier. (Contributed by NM, 3-Dec-2001)

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

Proof

Step	Hyp	Ref	Expression
1		euimmo	$$⊢\forall x\left(\exists !y\phi \to {\exists }^{*}y\phi \right)\to \left(\exists !x{\exists }^{*}y\phi \to {\exists }^{*}x\exists !y\phi \right)$$
2		eumo	$$⊢\exists !y\phi \to {\exists }^{*}y\phi$$
3	1 2	mpg	$$⊢\exists !x{\exists }^{*}y\phi \to {\exists }^{*}x\exists !y\phi$$