![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
Mirrors > Home > MPE Home > Th. List > df-wun | Structured version Unicode version |
Description: The class of all weak universes. A weak universe is a nonempty transitive class closed under union, pairing, and powerset. The advantage of a weak universe over a Grothendieck universe is that weak universes satisfy the analogue uniwun 9010 of grothtsk 9105 in ZFC. (Contributed by Mario Carneiro, 2-Jan-2017.) |
Ref | Expression |
---|---|
df-wun |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cwun 8970 |
. 2
![]() | |
2 | vu |
. . . . . 6
![]() ![]() | |
3 | 2 | cv 1369 |
. . . . 5
![]() ![]() |
4 | 3 | wtr 4485 |
. . . 4
![]() ![]() ![]() |
5 | c0 3737 |
. . . . 5
![]() ![]() | |
6 | 3, 5 | wne 2644 |
. . . 4
![]() ![]() ![]() ![]() |
7 | vx |
. . . . . . . . 9
![]() ![]() | |
8 | 7 | cv 1369 |
. . . . . . . 8
![]() ![]() |
9 | 8 | cuni 4191 |
. . . . . . 7
![]() ![]() ![]() |
10 | 9, 3 | wcel 1758 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() |
11 | 8 | cpw 3960 |
. . . . . . 7
![]() ![]() ![]() |
12 | 11, 3 | wcel 1758 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() |
13 | vy |
. . . . . . . . . 10
![]() ![]() | |
14 | 13 | cv 1369 |
. . . . . . . . 9
![]() ![]() |
15 | 8, 14 | cpr 3979 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() |
16 | 15, 3 | wcel 1758 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 16, 13, 3 | wral 2795 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | 10, 12, 17 | w3a 965 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | 18, 7, 3 | wral 2795 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | 4, 6, 19 | w3a 965 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
21 | 20, 2 | cab 2436 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 1, 21 | wceq 1370 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff setvar class |
This definition is referenced by: iswun 8974 |
Copyright terms: Public domain | W3C validator |