Theorem nn0readdcl

Description: Closure law for addition of reals, restricted to nonnegative integers. (Contributed by Alexander van der Vekens, 6-Apr-2018)

	Ref	Expression
Assertion	nn0readdcl	$$⊢\left(A\in {\mathbb{N}}_0\wedge B\in {\mathbb{N}}_0\right)\to A+B\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		nn0addcl	$$⊢\left(A\in {\mathbb{N}}_0\wedge B\in {\mathbb{N}}_0\right)\to A+B\in {\mathbb{N}}_0$$
2	1	nn0red	$$⊢\left(A\in {\mathbb{N}}_0\wedge B\in {\mathbb{N}}_0\right)\to A+B\in ℝ$$