Theorem moexexv

Description: "At most one" double quantification. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker moexexvw when possible. (Contributed by NM, 26-Jan-1997) (New usage is discouraged.)

	Ref	Expression
Assertion	moexexv	$$⊢\left({\exists }^{*}x\phi \wedge \forall x{\exists }^{*}y\psi \right)\to {\exists }^{*}y\exists x\left(\phi \wedge \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nfv	$$⊢Ⅎy\phi$$
2	1	moexex	$$⊢\left({\exists }^{*}x\phi \wedge \forall x{\exists }^{*}y\psi \right)\to {\exists }^{*}y\exists x\left(\phi \wedge \psi \right)$$