Theorem numnncl

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

	Ref	Expression
Hypotheses	numnncl.1	|- T e. NN0
	numnncl.2	|- A e. NN0
	numnncl.3	|- B e. NN
Assertion	numnncl	|- ( ( T x. A ) + B ) e. NN

Proof

Step	Hyp	Ref	Expression
1		numnncl.1	|- T e. NN0
2		numnncl.2	|- A e. NN0
3		numnncl.3	|- B e. NN
4	1 2	nn0mulcli	|- ( T x. A ) e. NN0
5		nn0nnaddcl	|- ( ( ( T x. A ) e. NN0 /\ B e. NN ) -> ( ( T x. A ) + B ) e. NN )
6	4 3 5	mp2an	|- ( ( T x. A ) + B ) e. NN