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Mirrors > Home > NFE Home > Th. List > df-ltfin | Unicode version |
Description: Define the less than relationship for finite cardinals. Definition from [Rosser] p. 527. (Contributed by SF, 12-Jan-2015.) |
Ref | Expression |
---|---|
df-ltfin |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cltfin 4434 |
. 2
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2 | vx |
. . . . . . . 8
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3 | 2 | cv 1641 |
. . . . . . 7
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4 | vm |
. . . . . . . . 9
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5 | 4 | cv 1641 |
. . . . . . . 8
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6 | vn |
. . . . . . . . 9
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7 | 6 | cv 1641 |
. . . . . . . 8
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8 | 5, 7 | copk 4058 |
. . . . . . 7
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9 | 3, 8 | wceq 1642 |
. . . . . 6
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10 | c0 3551 |
. . . . . . . 8
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11 | 5, 10 | wne 2517 |
. . . . . . 7
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12 | vp |
. . . . . . . . . . . 12
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13 | 12 | cv 1641 |
. . . . . . . . . . 11
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14 | 5, 13 | cplc 4376 |
. . . . . . . . . 10
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15 | c1c 4135 |
. . . . . . . . . 10
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16 | 14, 15 | cplc 4376 |
. . . . . . . . 9
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17 | 7, 16 | wceq 1642 |
. . . . . . . 8
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18 | cnnc 4374 |
. . . . . . . 8
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19 | 17, 12, 18 | wrex 2616 |
. . . . . . 7
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20 | 11, 19 | wa 358 |
. . . . . 6
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21 | 9, 20 | wa 358 |
. . . . 5
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22 | 21, 6 | wex 1541 |
. . . 4
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23 | 22, 4 | wex 1541 |
. . 3
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24 | 23, 2 | cab 2339 |
. 2
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25 | 1, 24 | wceq 1642 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: opkltfing 4450 ltfinex 4465 |
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