Step | Hyp | Ref
| Expression |
1 | | ctcph 24684 |
. 2
class
toβPreHil |
2 | | vw |
. . 3
setvar π€ |
3 | | cvv 3475 |
. . 3
class
V |
4 | 2 | cv 1541 |
. . . 4
class π€ |
5 | | vx |
. . . . 5
setvar π₯ |
6 | | cbs 17144 |
. . . . . 6
class
Base |
7 | 4, 6 | cfv 6544 |
. . . . 5
class
(Baseβπ€) |
8 | 5 | cv 1541 |
. . . . . . 7
class π₯ |
9 | | cip 17202 |
. . . . . . . 8
class
Β·π |
10 | 4, 9 | cfv 6544 |
. . . . . . 7
class
(Β·πβπ€) |
11 | 8, 8, 10 | co 7409 |
. . . . . 6
class (π₯(Β·πβπ€)π₯) |
12 | | csqrt 15180 |
. . . . . 6
class
β |
13 | 11, 12 | cfv 6544 |
. . . . 5
class
(ββ(π₯(Β·πβπ€)π₯)) |
14 | 5, 7, 13 | cmpt 5232 |
. . . 4
class (π₯ β (Baseβπ€) β¦ (ββ(π₯(Β·πβπ€)π₯))) |
15 | | ctng 24087 |
. . . 4
class
toNrmGrp |
16 | 4, 14, 15 | co 7409 |
. . 3
class (π€ toNrmGrp (π₯ β (Baseβπ€) β¦ (ββ(π₯(Β·πβπ€)π₯)))) |
17 | 2, 3, 16 | cmpt 5232 |
. 2
class (π€ β V β¦ (π€ toNrmGrp (π₯ β (Baseβπ€) β¦ (ββ(π₯(Β·πβπ€)π₯))))) |
18 | 1, 17 | wceq 1542 |
1
wff
toβPreHil = (π€
β V β¦ (π€
toNrmGrp (π₯ β
(Baseβπ€) β¦
(ββ(π₯(Β·πβπ€)π₯))))) |