Theorem recidzi

Description: Multiplication of a number and its reciprocal. (Contributed by NM, 14-May-1999)

	Ref	Expression
Hypothesis	divclz.1	$$⊢A\in ℂ$$
Assertion	recidzi	$$⊢A\ne 0\to A\left(\frac{1}{A}\right)=1$$

Proof

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