Theorem exdistr

Description: Distribution of existential quantifiers. See also exdistrv . (Contributed by NM, 9-Mar-1995)

	Ref	Expression
Assertion	exdistr	$$⊢\exists x\exists y\left(\phi \wedge \psi \right)\leftrightarrow \exists x\left(\phi \wedge \exists y\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		19.42v	$$⊢\exists y\left(\phi \wedge \psi \right)\leftrightarrow \left(\phi \wedge \exists y\psi \right)$$
2	1	exbii	$$⊢\exists x\exists y\left(\phi \wedge \psi \right)\leftrightarrow \exists x\left(\phi \wedge \exists y\psi \right)$$