Detailed syntax breakdown of Definition df-ascl
| Step | Hyp | Ref
| Expression |
| 1 | | cascl 21872 |
. 2
class
algSc |
| 2 | | vw |
. . 3
setvar 𝑤 |
| 3 | | cvv 3480 |
. . 3
class
V |
| 4 | | vx |
. . . 4
setvar 𝑥 |
| 5 | 2 | cv 1539 |
. . . . . 6
class 𝑤 |
| 6 | | csca 17300 |
. . . . . 6
class
Scalar |
| 7 | 5, 6 | cfv 6561 |
. . . . 5
class
(Scalar‘𝑤) |
| 8 | | cbs 17247 |
. . . . 5
class
Base |
| 9 | 7, 8 | cfv 6561 |
. . . 4
class
(Base‘(Scalar‘𝑤)) |
| 10 | 4 | cv 1539 |
. . . . 5
class 𝑥 |
| 11 | | cur 20178 |
. . . . . 6
class
1r |
| 12 | 5, 11 | cfv 6561 |
. . . . 5
class
(1r‘𝑤) |
| 13 | | cvsca 17301 |
. . . . . 6
class
·𝑠 |
| 14 | 5, 13 | cfv 6561 |
. . . . 5
class (
·𝑠 ‘𝑤) |
| 15 | 10, 12, 14 | co 7431 |
. . . 4
class (𝑥(
·𝑠 ‘𝑤)(1r‘𝑤)) |
| 16 | 4, 9, 15 | cmpt 5225 |
. . 3
class (𝑥 ∈
(Base‘(Scalar‘𝑤)) ↦ (𝑥( ·𝑠
‘𝑤)(1r‘𝑤))) |
| 17 | 2, 3, 16 | cmpt 5225 |
. 2
class (𝑤 ∈ V ↦ (𝑥 ∈
(Base‘(Scalar‘𝑤)) ↦ (𝑥( ·𝑠
‘𝑤)(1r‘𝑤)))) |
| 18 | 1, 17 | wceq 1540 |
1
wff algSc =
(𝑤 ∈ V ↦ (𝑥 ∈
(Base‘(Scalar‘𝑤)) ↦ (𝑥( ·𝑠
‘𝑤)(1r‘𝑤)))) |