Detailed syntax breakdown of Definition df-ascl
Step | Hyp | Ref
| Expression |
1 | | cascl 20668 |
. 2
class
algSc |
2 | | vw |
. . 3
setvar 𝑤 |
3 | | cvv 3398 |
. . 3
class
V |
4 | | vx |
. . . 4
setvar 𝑥 |
5 | 2 | cv 1541 |
. . . . . 6
class 𝑤 |
6 | | csca 16671 |
. . . . . 6
class
Scalar |
7 | 5, 6 | cfv 6339 |
. . . . 5
class
(Scalar‘𝑤) |
8 | | cbs 16586 |
. . . . 5
class
Base |
9 | 7, 8 | cfv 6339 |
. . . 4
class
(Base‘(Scalar‘𝑤)) |
10 | 4 | cv 1541 |
. . . . 5
class 𝑥 |
11 | | cur 19370 |
. . . . . 6
class
1r |
12 | 5, 11 | cfv 6339 |
. . . . 5
class
(1r‘𝑤) |
13 | | cvsca 16672 |
. . . . . 6
class
·𝑠 |
14 | 5, 13 | cfv 6339 |
. . . . 5
class (
·𝑠 ‘𝑤) |
15 | 10, 12, 14 | co 7170 |
. . . 4
class (𝑥(
·𝑠 ‘𝑤)(1r‘𝑤)) |
16 | 4, 9, 15 | cmpt 5110 |
. . 3
class (𝑥 ∈
(Base‘(Scalar‘𝑤)) ↦ (𝑥( ·𝑠
‘𝑤)(1r‘𝑤))) |
17 | 2, 3, 16 | cmpt 5110 |
. 2
class (𝑤 ∈ V ↦ (𝑥 ∈
(Base‘(Scalar‘𝑤)) ↦ (𝑥( ·𝑠
‘𝑤)(1r‘𝑤)))) |
18 | 1, 17 | wceq 1542 |
1
wff algSc =
(𝑤 ∈ V ↦ (𝑥 ∈
(Base‘(Scalar‘𝑤)) ↦ (𝑥( ·𝑠
‘𝑤)(1r‘𝑤)))) |