Mathbox for Stefan O'Rear |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > df-lnm | Structured version Visualization version Unicode version |
Description: A left-module is Noetherian iff it is hereditarily finitely generated. (Contributed by Stefan O'Rear, 12-Dec-2014.) |
Ref | Expression |
---|---|
df-lnm | LNoeM ↾s LFinGen |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clnm 37645 | . 2 LNoeM | |
2 | vw | . . . . . . 7 | |
3 | 2 | cv 1482 | . . . . . 6 |
4 | vi | . . . . . . 7 | |
5 | 4 | cv 1482 | . . . . . 6 |
6 | cress 15858 | . . . . . 6 ↾s | |
7 | 3, 5, 6 | co 6650 | . . . . 5 ↾s |
8 | clfig 37637 | . . . . 5 LFinGen | |
9 | 7, 8 | wcel 1990 | . . . 4 ↾s LFinGen |
10 | clss 18932 | . . . . 5 | |
11 | 3, 10 | cfv 5888 | . . . 4 |
12 | 9, 4, 11 | wral 2912 | . . 3 ↾s LFinGen |
13 | clmod 18863 | . . 3 | |
14 | 12, 2, 13 | crab 2916 | . 2 ↾s LFinGen |
15 | 1, 14 | wceq 1483 | 1 LNoeM ↾s LFinGen |
Colors of variables: wff setvar class |
This definition is referenced by: islnm 37647 |
Copyright terms: Public domain | W3C validator |