Theorem exancom

Description: Commutation of conjunction inside an existential quantifier. (Contributed by NM, 18-Aug-1993)

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

Proof

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