Theorem 3impdi

Description: Importation inference (undistribute conjunction). (Contributed by NM, 14-Aug-1995)

	Ref	Expression
Hypothesis	3impdi.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \left(\phi \wedge \chi \right)\right)\to \theta$$
Assertion	3impdi	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		3impdi.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \left(\phi \wedge \chi \right)\right)\to \theta$$
2	1	anandis	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \right)\right)\to \theta$$
3	2	3impb	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$