Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > df-ref | Structured version Visualization version Unicode version |
Description: Define the refinement relation. (Contributed by Jeff Hankins, 18-Jan-2010.) |
Ref | Expression |
---|---|
df-ref |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cref 21305 | . 2 | |
2 | vy | . . . . . . 7 | |
3 | 2 | cv 1482 | . . . . . 6 |
4 | 3 | cuni 4436 | . . . . 5 |
5 | vx | . . . . . . 7 | |
6 | 5 | cv 1482 | . . . . . 6 |
7 | 6 | cuni 4436 | . . . . 5 |
8 | 4, 7 | wceq 1483 | . . . 4 |
9 | vz | . . . . . . . 8 | |
10 | 9 | cv 1482 | . . . . . . 7 |
11 | vw | . . . . . . . 8 | |
12 | 11 | cv 1482 | . . . . . . 7 |
13 | 10, 12 | wss 3574 | . . . . . 6 |
14 | 13, 11, 3 | wrex 2913 | . . . . 5 |
15 | 14, 9, 6 | wral 2912 | . . . 4 |
16 | 8, 15 | wa 384 | . . 3 |
17 | 16, 5, 2 | copab 4712 | . 2 |
18 | 1, 17 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: refrel 21311 isref 21312 |
Copyright terms: Public domain | W3C validator |