Theorem recidi

Description: Multiplication of a number and its reciprocal. (Contributed by NM, 9-Feb-1995)

	Ref	Expression
Hypotheses	divclz.1	$$⊢A\in ℂ$$
	reccl.2	$$⊢A\ne 0$$
Assertion	recidi	$$⊢A\left(\frac{1}{A}\right)=1$$

Proof

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