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Definition df-dec 12714
Description: Define the "decimal constructor", which is used to build up "decimal integers" or "numeric terms" in base 10. For example, (1000 + 2000) = 3000 1kp2ke3k 30274. (Contributed by Mario Carneiro, 17-Apr-2015.) (Revised by AV, 1-Aug-2021.)
Assertion
Ref Expression
df-dec ๐ด๐ต = (((9 + 1) ยท ๐ด) + ๐ต)

Detailed syntax breakdown of Definition df-dec
StepHypRef Expression
1 cA . . 3 class ๐ด
2 cB . . 3 class ๐ต
31, 2cdc 12713 . 2 class ๐ด๐ต
4 c9 12310 . . . . 5 class 9
5 c1 11145 . . . . 5 class 1
6 caddc 11147 . . . . 5 class +
74, 5, 6co 7424 . . . 4 class (9 + 1)
8 cmul 11149 . . . 4 class ยท
97, 1, 8co 7424 . . 3 class ((9 + 1) ยท ๐ด)
109, 2, 6co 7424 . 2 class (((9 + 1) ยท ๐ด) + ๐ต)
113, 10wceq 1533 1 wff ๐ด๐ต = (((9 + 1) ยท ๐ด) + ๐ต)
Colors of variables: wff setvar class
This definition is referenced by:  9p1e10  12715  dfdec10  12716  decex  12717  deceq1  12718  deceq2  12719  deccl  12728  10re  12732  deccarry  46693
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