Definition df-dec 8478

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 10562. (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 8477	. 2 class ; A B
4		c9 8096	. . . . 5 class 9
5		c1 6982	. . . . 5 class 1
6		caddc 6984	. . . . 5 class +
7	4, 5, 6	co 5532	. . . 4 class ( 9 + 1 )
8		cmul 6986	. . . 4 class x.
9	7, 1, 8	co 5532	. . 3 class ( ( 9 + 1 ) x. A )
10	9, 2, 6	co 5532	. 2 class ( ( ( 9 + 1 ) x. A ) + B )
11	3, 10	wceq 1284	1 wff ; A B = ( ( ( 9 + 1 ) x. A ) + B )

This definition is referenced by:  9p1e10  8479  dfdec10  8480  deceq1  8481  deceq2  8482  deccl  8491