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Mirrors > Home > MPE Home > Th. List > df-chr | Structured version Visualization version GIF version |
Description: The characteristic of a ring is the smallest positive integer which is equal to 0 when interpreted in the ring, or 0 if there is no such positive integer. (Contributed by Stefan O'Rear, 5-Sep-2015.) |
Ref | Expression |
---|---|
df-chr | ⊢ chr = (𝑔 ∈ V ↦ ((od‘𝑔)‘(1r‘𝑔))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cchr 20501 | . 2 class chr | |
2 | vg | . . 3 setvar 𝑔 | |
3 | cvv 3423 | . . 3 class V | |
4 | 2 | cv 1542 | . . . . 5 class 𝑔 |
5 | cur 19549 | . . . . 5 class 1r | |
6 | 4, 5 | cfv 6401 | . . . 4 class (1r‘𝑔) |
7 | cod 18949 | . . . . 5 class od | |
8 | 4, 7 | cfv 6401 | . . . 4 class (od‘𝑔) |
9 | 6, 8 | cfv 6401 | . . 3 class ((od‘𝑔)‘(1r‘𝑔)) |
10 | 2, 3, 9 | cmpt 5152 | . 2 class (𝑔 ∈ V ↦ ((od‘𝑔)‘(1r‘𝑔))) |
11 | 1, 10 | wceq 1543 | 1 wff chr = (𝑔 ∈ V ↦ ((od‘𝑔)‘(1r‘𝑔))) |
Colors of variables: wff setvar class |
This definition is referenced by: chrval 20523 |
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