Theorem 19.42vvvOLD

Description: Obsolete version of 19.42vvv as of 27-Aug-2023. (Contributed by NM, 21-Sep-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	19.42vvvOLD	$$⊢\exists x\exists y\exists z\left(\phi \wedge \psi \right)\leftrightarrow \left(\phi \wedge \exists x\exists y\exists z\psi \right)$$

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	$$⊢\exists x\exists y\exists z\left(\phi \wedge \psi \right)\leftrightarrow \exists x\left(\phi \wedge \exists y\exists z\psi \right)$$
3		19.42v	$$⊢\exists x\left(\phi \wedge \exists y\exists z\psi \right)\leftrightarrow \left(\phi \wedge \exists x\exists y\exists z\psi \right)$$
4	2 3	bitri	$$⊢\exists x\exists y\exists z\left(\phi \wedge \psi \right)\leftrightarrow \left(\phi \wedge \exists x\exists y\exists z\psi \right)$$