Theorem numnncl2

Description: Closure for a decimal integer (zero units place). (Contributed by Mario Carneiro, 9-Mar-2015)

	Ref	Expression
Hypotheses	numnncl2.1	|- T e. NN
	numnncl2.2	|- A e. NN
Assertion	numnncl2	|- ( ( T x. A ) + 0 ) e. NN

Proof

Step	Hyp	Ref	Expression
1		numnncl2.1	|- T e. NN
2		numnncl2.2	|- A e. NN
3	1 2	nnmulcli	|- ( T x. A ) e. NN
4	3	nncni	|- ( T x. A ) e. CC
5	4	addid1i	|- ( ( T x. A ) + 0 ) = ( T x. A )
6	5 3	eqeltri	|- ( ( T x. A ) + 0 ) e. NN