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Mirrors > Home > ILE Home > Th. List > df-sub | Unicode version |
Description: Define subtraction. Theorem subval 7922 shows its value (and describes how this definition works), theorem subaddi 8017 relates it to addition, and theorems subcli 8006 and resubcli 7993 prove its closure laws. (Contributed by NM, 26-Nov-1994.) |
Ref | Expression |
---|---|
df-sub |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cmin 7901 | . 2 | |
2 | vx | . . 3 | |
3 | vy | . . 3 | |
4 | cc 7586 | . . 3 | |
5 | 3 | cv 1315 | . . . . . 6 |
6 | vz | . . . . . . 7 | |
7 | 6 | cv 1315 | . . . . . 6 |
8 | caddc 7591 | . . . . . 6 | |
9 | 5, 7, 8 | co 5742 | . . . . 5 |
10 | 2 | cv 1315 | . . . . 5 |
11 | 9, 10 | wceq 1316 | . . . 4 |
12 | 11, 6, 4 | crio 5697 | . . 3 |
13 | 2, 3, 4, 4, 12 | cmpo 5744 | . 2 |
14 | 1, 13 | wceq 1316 | 1 |
Colors of variables: wff set class |
This definition is referenced by: subval 7922 subf 7932 |
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