MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-dec Structured version   Visualization version   GIF version

Definition df-dec 11756
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 27630. (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 11755 . 2 class 𝐴𝐵
4 c9 11359 . . . . 5 class 9
5 c1 10218 . . . . 5 class 1
6 caddc 10220 . . . . 5 class +
74, 5, 6co 6870 . . . 4 class (9 + 1)
8 cmul 10222 . . . 4 class ·
97, 1, 8co 6870 . . 3 class ((9 + 1) · 𝐴)
109, 2, 6co 6870 . 2 class (((9 + 1) · 𝐴) + 𝐵)
113, 10wceq 1637 1 wff 𝐴𝐵 = (((9 + 1) · 𝐴) + 𝐵)
Colors of variables: wff setvar class
This definition is referenced by:  9p1e10  11757  dfdec10  11758  decex  11759  deceq1  11760  deceq2  11761  deccl  11770  deccarry  41890
  Copyright terms: Public domain W3C validator