Theorem deccl

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

	Ref	Expression
Hypotheses	deccl.1	$$⊢A\in {\mathbb{N}}_0$$
	deccl.2	$$⊢B\in {\mathbb{N}}_0$$
Assertion	deccl	Could not format assertion : No typesetting found for |- ; A B e. NN0 with typecode |-

Proof

Step	Hyp	Ref	Expression
1		deccl.1	$$⊢A\in {\mathbb{N}}_0$$
2		deccl.2	$$⊢B\in {\mathbb{N}}_0$$
3		df-dec	Could not format ; A B = ( ( ( 9 + 1 ) x. A ) + B ) : No typesetting found for |- ; A B = ( ( ( 9 + 1 ) x. A ) + B ) with typecode |-
4		9nn0	$$⊢9\in {\mathbb{N}}_0$$
5		1nn0	$$⊢1\in {\mathbb{N}}_0$$
6	4 5	nn0addcli	$$⊢9+1\in {\mathbb{N}}_0$$
7	6 1 2	numcl	$$⊢\left(9+1\right)A+B\in {\mathbb{N}}_0$$
8	3 7	eqeltri	Could not format ; A B e. NN0 : No typesetting found for |- ; A B e. NN0 with typecode |-