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Mirrors > Home > MPE Home > Th. List > df-dec | Structured version Visualization version GIF version |
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 26695. (Contributed by Mario Carneiro, 17-Apr-2015.) (Revised by AV, 1-Aug-2021.) |
Ref | Expression |
---|---|
df-dec | ⊢ ;𝐴𝐵 = (((9 + 1) · 𝐴) + 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class 𝐴 | |
2 | cB | . . 3 class 𝐵 | |
3 | 1, 2 | cdc 11369 | . 2 class ;𝐴𝐵 |
4 | c9 10954 | . . . . 5 class 9 | |
5 | c1 9816 | . . . . 5 class 1 | |
6 | caddc 9818 | . . . . 5 class + | |
7 | 4, 5, 6 | co 6549 | . . . 4 class (9 + 1) |
8 | cmul 9820 | . . . 4 class · | |
9 | 7, 1, 8 | co 6549 | . . 3 class ((9 + 1) · 𝐴) |
10 | 9, 2, 6 | co 6549 | . 2 class (((9 + 1) · 𝐴) + 𝐵) |
11 | 3, 10 | wceq 1475 | 1 wff ;𝐴𝐵 = (((9 + 1) · 𝐴) + 𝐵) |
Colors of variables: wff setvar class |
This definition is referenced by: dfdecOLD 11371 9p1e10 11372 dfdec10 11373 decex 11374 deceq1 11376 deceq2 11378 deccl 11388 deccarry 39941 |
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