Theorem readdcli

Description: Closure law for addition of reals. (Contributed by NM, 17-Jan-1997)

	Ref	Expression
Hypotheses	recni.1	$$⊢A\in ℝ$$
	axri.2	$$⊢B\in ℝ$$
Assertion	readdcli	$$⊢A+B\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		recni.1	$$⊢A\in ℝ$$
2		axri.2	$$⊢B\in ℝ$$
3		readdcl	$$⊢\left(A\in ℝ\wedge B\in ℝ\right)\to A+B\in ℝ$$
4	1 2 3	mp2an	$$⊢A+B\in ℝ$$