Theorem 19.40

Description: Theorem 19.40 of Margaris p. 90. (Contributed by NM, 26-May-1993)

	Ref	Expression
Assertion	19.40	$$⊢\exists x\left(\phi \wedge \psi \right)\to \left(\exists x\phi \wedge \exists x\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		exsimpl	$$⊢\exists x\left(\phi \wedge \psi \right)\to \exists x\phi$$
2		exsimpr	$$⊢\exists x\left(\phi \wedge \psi \right)\to \exists x\psi$$
3	1 2	jca	$$⊢\exists x\left(\phi \wedge \psi \right)\to \left(\exists x\phi \wedge \exists x\psi \right)$$