Theorem resubcld

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

	Ref	Expression
Hypotheses	renegcld.1	$$⊢\phi \to A\in ℝ$$
	resubcld.2	$$⊢\phi \to B\in ℝ$$
Assertion	resubcld	$$⊢\phi \to A-B\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		renegcld.1	$$⊢\phi \to A\in ℝ$$
2		resubcld.2	$$⊢\phi \to B\in ℝ$$
3		resubcl	$$⊢\left(A\in ℝ\wedge B\in ℝ\right)\to A-B\in ℝ$$
4	1 2 3	syl2anc	$$⊢\phi \to A-B\in ℝ$$