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Definition df-dec 12679
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 30204. (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 12678 . 2 class ๐ด๐ต
4 c9 12275 . . . . 5 class 9
5 c1 11110 . . . . 5 class 1
6 caddc 11112 . . . . 5 class +
74, 5, 6co 7404 . . . 4 class (9 + 1)
8 cmul 11114 . . . 4 class ยท
97, 1, 8co 7404 . . 3 class ((9 + 1) ยท ๐ด)
109, 2, 6co 7404 . 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  12680  dfdec10  12681  decex  12682  deceq1  12683  deceq2  12684  deccl  12693  10re  12697  deccarry  46572
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