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Mirrors > Home > NFE Home > Th. List > df-antisym | Unicode version |
Description: Define the set of all antisymmetric relationships over a base set. (Contributed by SF, 19-Feb-2015.) |
Ref | Expression |
---|---|
df-antisym | Antisym |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cantisym 5890 | . 2 Antisym | |
2 | vx | . . . . . . . . 9 | |
3 | 2 | cv 1641 | . . . . . . . 8 |
4 | vy | . . . . . . . . 9 | |
5 | 4 | cv 1641 | . . . . . . . 8 |
6 | vr | . . . . . . . . 9 | |
7 | 6 | cv 1641 | . . . . . . . 8 |
8 | 3, 5, 7 | wbr 4639 | . . . . . . 7 |
9 | 5, 3, 7 | wbr 4639 | . . . . . . 7 |
10 | 8, 9 | wa 358 | . . . . . 6 |
11 | 2, 4 | weq 1643 | . . . . . 6 |
12 | 10, 11 | wi 4 | . . . . 5 |
13 | va | . . . . . 6 | |
14 | 13 | cv 1641 | . . . . 5 |
15 | 12, 4, 14 | wral 2614 | . . . 4 |
16 | 15, 2, 14 | wral 2614 | . . 3 |
17 | 16, 6, 13 | copab 4622 | . 2 |
18 | 1, 17 | wceq 1642 | 1 Antisym |
Colors of variables: wff setvar class |
This definition is referenced by: antisymex 5912 antird 5928 antid 5929 |
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