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Metamath Proof Explorer

Theorem 2moexv

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

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

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