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Mirrors > Home > ILE Home > Th. List > df-div | Unicode version |
Description: Define division. Theorem divmulap 8592 relates it to multiplication, and divclap 8595 and redivclap 8648 prove its closure laws. (Contributed by NM, 2-Feb-1995.) Use divvalap 8591 instead. (Revised by Mario Carneiro, 1-Apr-2014.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-div |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdiv 8589 | . 2 | |
2 | vx | . . 3 | |
3 | vy | . . 3 | |
4 | cc 7772 | . . 3 | |
5 | cc0 7774 | . . . . 5 | |
6 | 5 | csn 3583 | . . . 4 |
7 | 4, 6 | cdif 3118 | . . 3 |
8 | 3 | cv 1347 | . . . . . 6 |
9 | vz | . . . . . . 7 | |
10 | 9 | cv 1347 | . . . . . 6 |
11 | cmul 7779 | . . . . . 6 | |
12 | 8, 10, 11 | co 5853 | . . . . 5 |
13 | 2 | cv 1347 | . . . . 5 |
14 | 12, 13 | wceq 1348 | . . . 4 |
15 | 14, 9, 4 | crio 5808 | . . 3 |
16 | 2, 3, 4, 7, 15 | cmpo 5855 | . 2 |
17 | 1, 16 | wceq 1348 | 1 |
Colors of variables: wff set class |
This definition is referenced by: divvalap 8591 divfnzn 9580 |
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