Detailed syntax breakdown of Definition df-lsp
Step | Hyp | Ref
| Expression |
1 | | clspn 19862 |
. 2
class
LSpan |
2 | | vw |
. . 3
setvar 𝑤 |
3 | | cvv 3398 |
. . 3
class
V |
4 | | vs |
. . . 4
setvar 𝑠 |
5 | 2 | cv 1541 |
. . . . . 6
class 𝑤 |
6 | | cbs 16586 |
. . . . . 6
class
Base |
7 | 5, 6 | cfv 6339 |
. . . . 5
class
(Base‘𝑤) |
8 | 7 | cpw 4488 |
. . . 4
class 𝒫
(Base‘𝑤) |
9 | 4 | cv 1541 |
. . . . . . 7
class 𝑠 |
10 | | vt |
. . . . . . . 8
setvar 𝑡 |
11 | 10 | cv 1541 |
. . . . . . 7
class 𝑡 |
12 | 9, 11 | wss 3843 |
. . . . . 6
wff 𝑠 ⊆ 𝑡 |
13 | | clss 19822 |
. . . . . . 7
class
LSubSp |
14 | 5, 13 | cfv 6339 |
. . . . . 6
class
(LSubSp‘𝑤) |
15 | 12, 10, 14 | crab 3057 |
. . . . 5
class {𝑡 ∈ (LSubSp‘𝑤) ∣ 𝑠 ⊆ 𝑡} |
16 | 15 | cint 4836 |
. . . 4
class ∩ {𝑡
∈ (LSubSp‘𝑤)
∣ 𝑠 ⊆ 𝑡} |
17 | 4, 8, 16 | cmpt 5110 |
. . 3
class (𝑠 ∈ 𝒫
(Base‘𝑤) ↦
∩ {𝑡 ∈ (LSubSp‘𝑤) ∣ 𝑠 ⊆ 𝑡}) |
18 | 2, 3, 17 | cmpt 5110 |
. 2
class (𝑤 ∈ V ↦ (𝑠 ∈ 𝒫
(Base‘𝑤) ↦
∩ {𝑡 ∈ (LSubSp‘𝑤) ∣ 𝑠 ⊆ 𝑡})) |
19 | 1, 18 | wceq 1542 |
1
wff LSpan =
(𝑤 ∈ V ↦ (𝑠 ∈ 𝒫
(Base‘𝑤) ↦
∩ {𝑡 ∈ (LSubSp‘𝑤) ∣ 𝑠 ⊆ 𝑡})) |