Theorem exsimpl

Description: Simplification of an existentially quantified conjunction. (Contributed by Rodolfo Medina, 25-Sep-2010) (Proof shortened by Andrew Salmon, 29-Jun-2011)

	Ref	Expression
Assertion	exsimpl	$$⊢\exists x\left(\phi \wedge \psi \right)\to \exists x\phi$$

Proof

Step	Hyp	Ref	Expression
1		simpl	$$⊢\left(\phi \wedge \psi \right)\to \phi$$
2	1	eximi	$$⊢\exists x\left(\phi \wedge \psi \right)\to \exists x\phi$$