Theorem recne0zi

Description: The reciprocal of a nonzero number is nonzero. (Contributed by NM, 14-May-1999)

	Ref	Expression
Hypothesis	divclz.1	$$⊢A\in ℂ$$
Assertion	recne0zi	$$⊢A\ne 0\to \frac{1}{A}\ne 0$$

Proof

Step	Hyp	Ref	Expression
1		divclz.1	$$⊢A\in ℂ$$
2		recne0	$$⊢\left(A\in ℂ\wedge A\ne 0\right)\to \frac{1}{A}\ne 0$$
3	1 2	mpan	$$⊢A\ne 0\to \frac{1}{A}\ne 0$$