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Mirrors > Home > ILE Home > Th. List > df-sub | Unicode version |
Description: Define subtraction. Theorem subval 7437 shows its value (and describes how this definition works), theorem subaddi 7532 relates it to addition, and theorems subcli 7521 and resubcli 7508 prove its closure laws. (Contributed by NM, 26-Nov-1994.) |
Ref | Expression |
---|---|
df-sub |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cmin 7416 |
. 2
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2 | vx |
. . 3
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3 | vy |
. . 3
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4 | cc 7111 |
. . 3
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5 | 3 | cv 1284 |
. . . . . 6
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6 | vz |
. . . . . . 7
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7 | 6 | cv 1284 |
. . . . . 6
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8 | caddc 7116 |
. . . . . 6
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9 | 5, 7, 8 | co 5564 |
. . . . 5
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10 | 2 | cv 1284 |
. . . . 5
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11 | 9, 10 | wceq 1285 |
. . . 4
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12 | 11, 6, 4 | crio 5519 |
. . 3
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13 | 2, 3, 4, 4, 12 | cmpt2 5566 |
. 2
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14 | 1, 13 | wceq 1285 |
1
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Colors of variables: wff set class |
This definition is referenced by: subval 7437 subf 7447 |
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