Step | Hyp | Ref
| Expression |
1 | | clinc 47173 |
. 2
class
linC |
2 | | vm |
. . 3
setvar π |
3 | | cvv 3474 |
. . 3
class
V |
4 | | vs |
. . . 4
setvar π |
5 | | vv |
. . . 4
setvar π£ |
6 | 2 | cv 1540 |
. . . . . . 7
class π |
7 | | csca 17204 |
. . . . . . 7
class
Scalar |
8 | 6, 7 | cfv 6543 |
. . . . . 6
class
(Scalarβπ) |
9 | | cbs 17148 |
. . . . . 6
class
Base |
10 | 8, 9 | cfv 6543 |
. . . . 5
class
(Baseβ(Scalarβπ)) |
11 | 5 | cv 1540 |
. . . . 5
class π£ |
12 | | cmap 8822 |
. . . . 5
class
βm |
13 | 10, 11, 12 | co 7411 |
. . . 4
class
((Baseβ(Scalarβπ)) βm π£) |
14 | 6, 9 | cfv 6543 |
. . . . 5
class
(Baseβπ) |
15 | 14 | cpw 4602 |
. . . 4
class π«
(Baseβπ) |
16 | | vx |
. . . . . 6
setvar π₯ |
17 | 16 | cv 1540 |
. . . . . . . 8
class π₯ |
18 | 4 | cv 1540 |
. . . . . . . 8
class π |
19 | 17, 18 | cfv 6543 |
. . . . . . 7
class (π βπ₯) |
20 | | cvsca 17205 |
. . . . . . . 8
class
Β·π |
21 | 6, 20 | cfv 6543 |
. . . . . . 7
class (
Β·π βπ) |
22 | 19, 17, 21 | co 7411 |
. . . . . 6
class ((π βπ₯)( Β·π
βπ)π₯) |
23 | 16, 11, 22 | cmpt 5231 |
. . . . 5
class (π₯ β π£ β¦ ((π βπ₯)( Β·π
βπ)π₯)) |
24 | | cgsu 17390 |
. . . . 5
class
Ξ£g |
25 | 6, 23, 24 | co 7411 |
. . . 4
class (π Ξ£g
(π₯ β π£ β¦ ((π βπ₯)( Β·π
βπ)π₯))) |
26 | 4, 5, 13, 15, 25 | cmpo 7413 |
. . 3
class (π β
((Baseβ(Scalarβπ)) βm π£), π£ β π« (Baseβπ) β¦ (π Ξ£g (π₯ β π£ β¦ ((π βπ₯)( Β·π
βπ)π₯)))) |
27 | 2, 3, 26 | cmpt 5231 |
. 2
class (π β V β¦ (π β
((Baseβ(Scalarβπ)) βm π£), π£ β π« (Baseβπ) β¦ (π Ξ£g (π₯ β π£ β¦ ((π βπ₯)( Β·π
βπ)π₯))))) |
28 | 1, 27 | wceq 1541 |
1
wff linC =
(π β V β¦ (π β
((Baseβ(Scalarβπ)) βm π£), π£ β π« (Baseβπ) β¦ (π Ξ£g (π₯ β π£ β¦ ((π βπ₯)( Β·π
βπ)π₯))))) |