Theorem 1p1times

Description: Two times a number. (Contributed by NM, 18-May-1999) (Revised by Mario Carneiro, 27-May-2016)

	Ref	Expression
Assertion	1p1times	$$⊢A\in ℂ\to \left(1+1\right)A=A+A$$

Proof

Step	Hyp	Ref	Expression
1		1cnd	$$⊢A\in ℂ\to 1\in ℂ$$
2		id	$$⊢A\in ℂ\to A\in ℂ$$
3		mulid2	$$⊢A\in ℂ\to 1A=A$$
4	3 3	oveq12d	$$⊢A\in ℂ\to 1A+1A=A+A$$
5	1 2 1 4	joinlmuladdmuld	$$⊢A\in ℂ\to \left(1+1\right)A=A+A$$