Theorem redivcli

Description: Closure law for division of reals. (Contributed by NM, 9-May-1999)

	Ref	Expression
Hypotheses	redivcl.1	|- A e. RR
	redivcl.2	|- B e. RR
	redivcl.3	|- B =/= 0
Assertion	redivcli	|- ( A / B ) e. RR

Proof

Step	Hyp	Ref	Expression
1		redivcl.1	|- A e. RR
2		redivcl.2	|- B e. RR
3		redivcl.3	|- B =/= 0
4	1 2	redivclzi	|- ( B =/= 0 -> ( A / B ) e. RR )
5	3 4	ax-mp	|- ( A / B ) e. RR