Theorem numcl

Description: Closure for a decimal integer (with units place). (Contributed by Mario Carneiro, 18-Feb-2014)

	Ref	Expression
Hypotheses	numnncl.1	$$⊢T\in {\mathbb{N}}_0$$
	numnncl.2	$$⊢A\in {\mathbb{N}}_0$$
	numcl.2	$$⊢B\in {\mathbb{N}}_0$$
Assertion	numcl	$$⊢TA+B\in {\mathbb{N}}_0$$

Proof

Step	Hyp	Ref	Expression
1		numnncl.1	$$⊢T\in {\mathbb{N}}_0$$
2		numnncl.2	$$⊢A\in {\mathbb{N}}_0$$
3		numcl.2	$$⊢B\in {\mathbb{N}}_0$$
4	1 2	nn0mulcli	$$⊢TA\in {\mathbb{N}}_0$$
5	4 3	nn0addcli	$$⊢TA+B\in {\mathbb{N}}_0$$