Theorem div0i

Description: Division into zero is zero. (Contributed by NM, 12-Aug-1999)

	Ref	Expression
Hypotheses	divclz.1	$$⊢A\in ℂ$$
	reccl.2	$$⊢A\ne 0$$
Assertion	div0i	$$⊢\frac{0}{A}=0$$

Proof

Step	Hyp	Ref	Expression
1		divclz.1	$$⊢A\in ℂ$$
2		reccl.2	$$⊢A\ne 0$$
3		div0	$$⊢\left(A\in ℂ\wedge A\ne 0\right)\to \frac{0}{A}=0$$
4	1 2 3	mp2an	$$⊢\frac{0}{A}=0$$