New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > df-spac | Unicode version |
Description: Define the special class generator for the disproof of the axiom of choice. Definition 6.1 of [Specker] p. 973. (Contributed by SF, 3-Mar-2015.) |
Ref | Expression |
---|---|
df-spac | Spac NC Clos1 NC NC 2c ↑c |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cspac 6273 | . 2 Spac | |
2 | vm | . . 3 | |
3 | cncs 6088 | . . 3 NC | |
4 | 2 | cv 1641 | . . . . 5 |
5 | 4 | csn 3737 | . . . 4 |
6 | vx | . . . . . . . 8 | |
7 | 6 | cv 1641 | . . . . . . 7 |
8 | 7, 3 | wcel 1710 | . . . . . 6 NC |
9 | vy | . . . . . . . 8 | |
10 | 9 | cv 1641 | . . . . . . 7 |
11 | 10, 3 | wcel 1710 | . . . . . 6 NC |
12 | c2c 6094 | . . . . . . . 8 2c | |
13 | cce 6096 | . . . . . . . 8 ↑c | |
14 | 12, 7, 13 | co 5525 | . . . . . . 7 2c ↑c |
15 | 10, 14 | wceq 1642 | . . . . . 6 2c ↑c |
16 | 8, 11, 15 | w3a 934 | . . . . 5 NC NC 2c ↑c |
17 | 16, 6, 9 | copab 4622 | . . . 4 NC NC 2c ↑c |
18 | 5, 17 | cclos1 5872 | . . 3 Clos1 NC NC 2c ↑c |
19 | 2, 3, 18 | cmpt 5651 | . 2 NC Clos1 NC NC 2c ↑c |
20 | 1, 19 | wceq 1642 | 1 Spac NC Clos1 NC NC 2c ↑c |
Colors of variables: wff setvar class |
This definition is referenced by: spacval 6282 fnspac 6283 |
Copyright terms: Public domain | W3C validator |