Theorem exdistr2

Description: Distribution of existential quantifiers. (Contributed by NM, 17-Mar-1995)

	Ref	Expression
Assertion	exdistr2	$$⊢\exists x\exists y\exists z\left(\phi \wedge \psi \right)\leftrightarrow \exists x\left(\phi \wedge \exists y\exists z\psi \right)$$

Proof

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