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Definition df-dec 9176
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 12925. (Contributed by Mario Carneiro, 17-Apr-2015.) (Revised by AV, 1-Aug-2021.)
Assertion
Ref Expression
df-dec 𝐴𝐵 = (((9 + 1) · 𝐴) + 𝐵)

Detailed syntax breakdown of Definition df-dec
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cB . . 3 class 𝐵
31, 2cdc 9175 . 2 class 𝐴𝐵
4 c9 8771 . . . . 5 class 9
5 c1 7614 . . . . 5 class 1
6 caddc 7616 . . . . 5 class +
74, 5, 6co 5767 . . . 4 class (9 + 1)
8 cmul 7618 . . . 4 class ·
97, 1, 8co 5767 . . 3 class ((9 + 1) · 𝐴)
109, 2, 6co 5767 . 2 class (((9 + 1) · 𝐴) + 𝐵)
113, 10wceq 1331 1 wff 𝐴𝐵 = (((9 + 1) · 𝐴) + 𝐵)
Colors of variables: wff set class
This definition is referenced by:  9p1e10  9177  dfdec10  9178  deceq1  9179  deceq2  9180  deccl  9189
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