Theorem divcan2i

Description: A cancellation law for division. (Contributed by NM, 9-Feb-1995)

	Ref	Expression
Hypotheses	divclz.1	$$⊢A\in ℂ$$
	divclz.2	$$⊢B\in ℂ$$
	divcl.3	$$⊢B\ne 0$$
Assertion	divcan2i	$$⊢B\left(\frac{A}{B}\right)=A$$

Proof

Step	Hyp	Ref	Expression
1		divclz.1	$$⊢A\in ℂ$$
2		divclz.2	$$⊢B\in ℂ$$
3		divcl.3	$$⊢B\ne 0$$
4	1 2	divcan2zi	$$⊢B\ne 0\to B\left(\frac{A}{B}\right)=A$$
5	3 4	ax-mp	$$⊢B\left(\frac{A}{B}\right)=A$$