Theorem half0

Description: Half of a number is zero iff the number is zero. (Contributed by NM, 20-Apr-2006)

	Ref	Expression
Assertion	half0	$$⊢A\in ℂ\to \left(\frac{A}{2}=0\leftrightarrow A=0\right)$$

Proof

Step	Hyp	Ref	Expression
1		2cn	$$⊢2\in ℂ$$
2		2ne0	$$⊢2\ne 0$$
3		diveq0	$$⊢\left(A\in ℂ\wedge 2\in ℂ\wedge 2\ne 0\right)\to \left(\frac{A}{2}=0\leftrightarrow A=0\right)$$
4	1 2 3	mp3an23	$$⊢A\in ℂ\to \left(\frac{A}{2}=0\leftrightarrow A=0\right)$$