Step | Hyp | Ref
| Expression |
1 | | clm 22722 |
. 2
class
βπ‘ |
2 | | vj |
. . 3
setvar π |
3 | | ctop 22387 |
. . 3
class
Top |
4 | | vf |
. . . . . . 7
setvar π |
5 | 4 | cv 1541 |
. . . . . 6
class π |
6 | 2 | cv 1541 |
. . . . . . . 8
class π |
7 | 6 | cuni 4908 |
. . . . . . 7
class βͺ π |
8 | | cc 11105 |
. . . . . . 7
class
β |
9 | | cpm 8818 |
. . . . . . 7
class
βpm |
10 | 7, 8, 9 | co 7406 |
. . . . . 6
class (βͺ π
βpm β) |
11 | 5, 10 | wcel 2107 |
. . . . 5
wff π β (βͺ π
βpm β) |
12 | | vx |
. . . . . . 7
setvar π₯ |
13 | 12 | cv 1541 |
. . . . . 6
class π₯ |
14 | 13, 7 | wcel 2107 |
. . . . 5
wff π₯ β βͺ π |
15 | | vu |
. . . . . . . 8
setvar π’ |
16 | 12, 15 | wel 2108 |
. . . . . . 7
wff π₯ β π’ |
17 | | vy |
. . . . . . . . . 10
setvar π¦ |
18 | 17 | cv 1541 |
. . . . . . . . 9
class π¦ |
19 | 15 | cv 1541 |
. . . . . . . . 9
class π’ |
20 | 5, 18 | cres 5678 |
. . . . . . . . 9
class (π βΎ π¦) |
21 | 18, 19, 20 | wf 6537 |
. . . . . . . 8
wff (π βΎ π¦):π¦βΆπ’ |
22 | | cuz 12819 |
. . . . . . . . 9
class
β€β₯ |
23 | 22 | crn 5677 |
. . . . . . . 8
class ran
β€β₯ |
24 | 21, 17, 23 | wrex 3071 |
. . . . . . 7
wff
βπ¦ β ran
β€β₯(π
βΎ π¦):π¦βΆπ’ |
25 | 16, 24 | wi 4 |
. . . . . 6
wff (π₯ β π’ β βπ¦ β ran β€β₯(π βΎ π¦):π¦βΆπ’) |
26 | 25, 15, 6 | wral 3062 |
. . . . 5
wff
βπ’ β
π (π₯ β π’ β βπ¦ β ran β€β₯(π βΎ π¦):π¦βΆπ’) |
27 | 11, 14, 26 | w3a 1088 |
. . . 4
wff (π β (βͺ π
βpm β) β§ π₯ β βͺ π β§ βπ’ β π (π₯ β π’ β βπ¦ β ran β€β₯(π βΎ π¦):π¦βΆπ’)) |
28 | 27, 4, 12 | copab 5210 |
. . 3
class
{β¨π, π₯β© β£ (π β (βͺ π
βpm β) β§ π₯ β βͺ π β§ βπ’ β π (π₯ β π’ β βπ¦ β ran β€β₯(π βΎ π¦):π¦βΆπ’))} |
29 | 2, 3, 28 | cmpt 5231 |
. 2
class (π β Top β¦ {β¨π, π₯β© β£ (π β (βͺ π βpm β)
β§ π₯ β βͺ π
β§ βπ’ β
π (π₯ β π’ β βπ¦ β ran β€β₯(π βΎ π¦):π¦βΆπ’))}) |
30 | 1, 29 | wceq 1542 |
1
wff
βπ‘ = (π β Top β¦ {β¨π, π₯β© β£ (π β (βͺ π βpm β)
β§ π₯ β βͺ π
β§ βπ’ β
π (π₯ β π’ β βπ¦ β ran β€β₯(π βΎ π¦):π¦βΆπ’))}) |