Theorem mulid2

Description: Identity law for multiplication. See mulid1 for commuted version. (Contributed by NM, 8-Oct-1999)

	Ref	Expression
Assertion	mulid2	$$⊢A\in ℂ\to 1A=A$$

Proof

Step	Hyp	Ref	Expression
1		ax-1cn	$$⊢1\in ℂ$$
2		mulcom	$$⊢\left(1\in ℂ\wedge A\in ℂ\right)\to 1A=A\cdot 1$$
3	1 2	mpan	$$⊢A\in ℂ\to 1A=A\cdot 1$$
4		mulid1	$$⊢A\in ℂ\to A\cdot 1=A$$
5	3 4	eqtrd	$$⊢A\in ℂ\to 1A=A$$