Theorem adddiri

Description: Distributive law (right-distributivity). (Contributed by NM, 16-Feb-1995)

	Ref	Expression
Hypotheses	axi.1	$$⊢A\in ℂ$$
	axi.2	$$⊢B\in ℂ$$
	axi.3	$$⊢C\in ℂ$$
Assertion	adddiri	$$⊢\left(A+B\right)C=AC+BC$$

Proof

Step	Hyp	Ref	Expression
1		axi.1	$$⊢A\in ℂ$$
2		axi.2	$$⊢B\in ℂ$$
3		axi.3	$$⊢C\in ℂ$$
4		adddir	$$⊢\left(A\in ℂ\wedge B\in ℂ\wedge C\in ℂ\right)\to \left(A+B\right)C=AC+BC$$
5	1 2 3 4	mp3an	$$⊢\left(A+B\right)C=AC+BC$$