Theorem 3impdir

Description: Importation inference (undistribute conjunction). (Contributed by NM, 20-Aug-1995)

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

Proof

Step	Hyp	Ref	Expression
1		3impdir.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \left(\chi \wedge \psi \right)\right)\to \theta$$
2	1	anandirs	$$⊢\left(\left(\phi \wedge \chi \right)\wedge \psi \right)\to \theta$$
3	2	3impa	$$⊢\left(\phi \wedge \chi \wedge \psi \right)\to \theta$$