Theorem imdistani

Description: Distribution of implication with conjunction. (Contributed by NM, 1-Aug-1994)

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

Proof

Step	Hyp	Ref	Expression
1		imdistani.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2	1	anc2li	$$⊢\phi \to \left(\psi \to \left(\phi \wedge \chi \right)\right)$$
3	2	imp	$$⊢\left(\phi \wedge \psi \right)\to \left(\phi \wedge \chi \right)$$