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Mirrors > Home > ILE Home > Th. List > df-div | Unicode version |
Description: Define division. Theorem divmulap 8621 relates it to multiplication, and divclap 8624 and redivclap 8677 prove its closure laws. (Contributed by NM, 2-Feb-1995.) Use divvalap 8620 instead. (Revised by Mario Carneiro, 1-Apr-2014.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-div |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdiv 8618 |
. 2
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2 | vx |
. . 3
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3 | vy |
. . 3
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4 | cc 7800 |
. . 3
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5 | cc0 7802 |
. . . . 5
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6 | 5 | csn 3591 |
. . . 4
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7 | 4, 6 | cdif 3126 |
. . 3
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8 | 3 | cv 1352 |
. . . . . 6
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9 | vz |
. . . . . . 7
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10 | 9 | cv 1352 |
. . . . . 6
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11 | cmul 7807 |
. . . . . 6
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12 | 8, 10, 11 | co 5869 |
. . . . 5
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13 | 2 | cv 1352 |
. . . . 5
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14 | 12, 13 | wceq 1353 |
. . . 4
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15 | 14, 9, 4 | crio 5824 |
. . 3
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16 | 2, 3, 4, 7, 15 | cmpo 5871 |
. 2
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17 | 1, 16 | wceq 1353 |
1
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Colors of variables: wff set class |
This definition is referenced by: divvalap 8620 divfnzn 9610 |
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