Theorem redivcld

Description: Closure law for division of reals. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypotheses	redivcld.1	|- ( ph -> A e. RR )
	redivcld.2	|- ( ph -> B e. RR )
	redivcld.3	|- ( ph -> B =/= 0 )
Assertion	redivcld	|- ( ph -> ( A / B ) e. RR )

Proof

Step	Hyp	Ref	Expression
1		redivcld.1	|- ( ph -> A e. RR )
2		redivcld.2	|- ( ph -> B e. RR )
3		redivcld.3	|- ( ph -> B =/= 0 )
4		redivcl	|- ( ( A e. RR /\ B e. RR /\ B =/= 0 ) -> ( A / B ) e. RR )
5	1 2 3 4	syl3anc	|- ( ph -> ( A / B ) e. RR )