Definition df-dec 9673

Description: Define the "decimal constructor", which is used to build up "decimal integers" or "numeric terms" in base 1 0. For example, (;;; 1 0 0 0 + ;;; 2 0 0 0 ) = ;;; 3 0 0 0 1kp2ke3k 16438. (Contributed by Mario Carneiro, 17-Apr-2015.) (Revised by AV, 1-Aug-2021.)

Assertion

Ref	Expression
df-dec	|- ; A B = ( ( ( 9 + 1 ) x. A ) + B )

Detailed syntax breakdown of Definition df-dec

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cB	. . 3 class B
3	1, 2	cdc 9672	. 2 class ; A B
4		c9 9260	. . . . 5 class 9
5		c1 8093	. . . . 5 class 1
6		caddc 8095	. . . . 5 class +
7	4, 5, 6	co 6028	. . . 4 class ( 9 + 1 )
8		cmul 8097	. . . 4 class x.
9	7, 1, 8	co 6028	. . 3 class ( ( 9 + 1 ) x. A )
10	9, 2, 6	co 6028	. 2 class ( ( ( 9 + 1 ) x. A ) + B )
11	3, 10	wceq 1398	1 wff ; A B = ( ( ( 9 + 1 ) x. A ) + B )

This definition is referenced by:  9p1e10  9674  dfdec10  9675  deceq1  9676  deceq2  9677  deccl  9686