Theorem divcli

Description: Closure law for division. (Contributed by NM, 2-Feb-1995) (Revised by Mario Carneiro, 17-Feb-2014)

	Ref	Expression
Hypotheses	divclz.1	|- A e. CC
	divclz.2	|- B e. CC
	divcl.3	|- B =/= 0
Assertion	divcli	|- ( A / B ) e. CC

Proof

Step	Hyp	Ref	Expression
1		divclz.1	|- A e. CC
2		divclz.2	|- B e. CC
3		divcl.3	|- B =/= 0
4	1 2	divclzi	|- ( B =/= 0 -> ( A / B ) e. CC )
5	3 4	ax-mp	|- ( A / B ) e. CC