Theorem imdistanri

Description: Distribution of implication with conjunction. (Contributed by NM, 8-Jan-2002)

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

Proof

Step	Hyp	Ref	Expression
1		imdistanri.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2	1	com12	$$⊢\psi \to \left(\phi \to \chi \right)$$
3	2	impac	$$⊢\left(\psi \wedge \phi \right)\to \left(\chi \wedge \phi \right)$$