Theorem resubcld

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

	Ref	Expression
Hypotheses	renegcld.1	|- ( ph -> A e. RR )
	resubcld.2	|- ( ph -> B e. RR )
Assertion	resubcld	|- ( ph -> ( A - B ) e. RR )

Proof

Step	Hyp	Ref	Expression
1		renegcld.1	|- ( ph -> A e. RR )
2		resubcld.2	|- ( ph -> B e. RR )
3		resubcl	|- ( ( A e. RR /\ B e. RR ) -> ( A - B ) e. RR )
4	1 2 3	syl2anc	|- ( ph -> ( A - B ) e. RR )