Detailed syntax breakdown of Definition df-lnm
Step | Hyp | Ref
| Expression |
1 | | clnm 40603 |
. 2
class
LNoeM |
2 | | vw |
. . . . . . 7
setvar 𝑤 |
3 | 2 | cv 1542 |
. . . . . 6
class 𝑤 |
4 | | vi |
. . . . . . 7
setvar 𝑖 |
5 | 4 | cv 1542 |
. . . . . 6
class 𝑖 |
6 | | cress 16784 |
. . . . . 6
class
↾s |
7 | 3, 5, 6 | co 7213 |
. . . . 5
class (𝑤 ↾s 𝑖) |
8 | | clfig 40595 |
. . . . 5
class
LFinGen |
9 | 7, 8 | wcel 2110 |
. . . 4
wff (𝑤 ↾s 𝑖) ∈
LFinGen |
10 | | clss 19968 |
. . . . 5
class
LSubSp |
11 | 3, 10 | cfv 6380 |
. . . 4
class
(LSubSp‘𝑤) |
12 | 9, 4, 11 | wral 3061 |
. . 3
wff
∀𝑖 ∈
(LSubSp‘𝑤)(𝑤 ↾s 𝑖) ∈
LFinGen |
13 | | clmod 19899 |
. . 3
class
LMod |
14 | 12, 2, 13 | crab 3065 |
. 2
class {𝑤 ∈ LMod ∣
∀𝑖 ∈
(LSubSp‘𝑤)(𝑤 ↾s 𝑖) ∈
LFinGen} |
15 | 1, 14 | wceq 1543 |
1
wff LNoeM =
{𝑤 ∈ LMod ∣
∀𝑖 ∈
(LSubSp‘𝑤)(𝑤 ↾s 𝑖) ∈
LFinGen} |