Step | Hyp | Ref
| Expression |
1 | | cpclN 38753 |
. 2
class
PCl |
2 | | vk |
. . 3
setvar π |
3 | | cvv 3474 |
. . 3
class
V |
4 | | vx |
. . . 4
setvar π₯ |
5 | 2 | cv 1540 |
. . . . . 6
class π |
6 | | catm 38128 |
. . . . . 6
class
Atoms |
7 | 5, 6 | cfv 6543 |
. . . . 5
class
(Atomsβπ) |
8 | 7 | cpw 4602 |
. . . 4
class π«
(Atomsβπ) |
9 | 4 | cv 1540 |
. . . . . . 7
class π₯ |
10 | | vy |
. . . . . . . 8
setvar π¦ |
11 | 10 | cv 1540 |
. . . . . . 7
class π¦ |
12 | 9, 11 | wss 3948 |
. . . . . 6
wff π₯ β π¦ |
13 | | cpsubsp 38362 |
. . . . . . 7
class
PSubSp |
14 | 5, 13 | cfv 6543 |
. . . . . 6
class
(PSubSpβπ) |
15 | 12, 10, 14 | crab 3432 |
. . . . 5
class {π¦ β (PSubSpβπ) β£ π₯ β π¦} |
16 | 15 | cint 4950 |
. . . 4
class β© {π¦
β (PSubSpβπ)
β£ π₯ β π¦} |
17 | 4, 8, 16 | cmpt 5231 |
. . 3
class (π₯ β π«
(Atomsβπ) β¦
β© {π¦ β (PSubSpβπ) β£ π₯ β π¦}) |
18 | 2, 3, 17 | cmpt 5231 |
. 2
class (π β V β¦ (π₯ β π«
(Atomsβπ) β¦
β© {π¦ β (PSubSpβπ) β£ π₯ β π¦})) |
19 | 1, 18 | wceq 1541 |
1
wff PCl =
(π β V β¦ (π₯ β π«
(Atomsβπ) β¦
β© {π¦ β (PSubSpβπ) β£ π₯ β π¦})) |