Theorem decnncl

Description: Closure for a numeral. (Contributed by Mario Carneiro, 17-Apr-2015) (Revised by AV, 6-Sep-2021)

	Ref	Expression
Hypotheses	decnncl.1	|- A e. NN0
	decnncl.2	|- B e. NN
Assertion	decnncl	|- ; A B e. NN

Proof

Step	Hyp	Ref	Expression
1		decnncl.1	|- A e. NN0
2		decnncl.2	|- B e. NN
3		dfdec10	|- ; A B = ( ( ; 1 0 x. A ) + B )
4		10nn0	|- ; 1 0 e. NN0
5	4 1 2	numnncl	|- ( ( ; 1 0 x. A ) + B ) e. NN
6	3 5	eqeltri	|- ; A B e. NN