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Mirrors > Home > ILE Home > Th. List > f1ocnv2d | Unicode version |
Description: Describe an implicit one-to-one onto function. (Contributed by Mario Carneiro, 30-Apr-2015.) |
Ref | Expression |
---|---|
f1od.1 |
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f1o2d.2 |
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f1o2d.3 |
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f1o2d.4 |
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Ref | Expression |
---|---|
f1ocnv2d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1od.1 |
. 2
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2 | f1o2d.2 |
. 2
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3 | f1o2d.3 |
. 2
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4 | eleq1a 2184 |
. . . . . 6
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5 | 2, 4 | syl 14 |
. . . . 5
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6 | 5 | impr 374 |
. . . 4
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7 | f1o2d.4 |
. . . . . . . 8
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8 | 7 | biimpar 293 |
. . . . . . 7
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9 | 8 | exp42 366 |
. . . . . 6
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10 | 9 | com34 83 |
. . . . 5
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11 | 10 | imp32 255 |
. . . 4
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12 | 6, 11 | jcai 307 |
. . 3
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13 | eleq1a 2184 |
. . . . . 6
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14 | 3, 13 | syl 14 |
. . . . 5
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15 | 14 | impr 374 |
. . . 4
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16 | 7 | biimpa 292 |
. . . . . . . 8
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17 | 16 | exp42 366 |
. . . . . . 7
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18 | 17 | com23 78 |
. . . . . 6
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19 | 18 | com34 83 |
. . . . 5
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20 | 19 | imp32 255 |
. . . 4
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21 | 15, 20 | jcai 307 |
. . 3
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22 | 12, 21 | impbida 568 |
. 2
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23 | 1, 2, 3, 22 | f1ocnvd 5924 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-14 1473 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 ax-sep 4004 ax-pow 4056 ax-pr 4089 |
This theorem depends on definitions: df-bi 116 df-3an 945 df-tru 1315 df-nf 1418 df-sb 1717 df-eu 1976 df-mo 1977 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-ral 2393 df-rex 2394 df-v 2657 df-un 3039 df-in 3041 df-ss 3048 df-pw 3476 df-sn 3497 df-pr 3498 df-op 3500 df-br 3894 df-opab 3948 df-mpt 3949 df-id 4173 df-xp 4503 df-rel 4504 df-cnv 4505 df-co 4506 df-dm 4507 df-rn 4508 df-fun 5081 df-fn 5082 df-f 5083 df-f1 5084 df-fo 5085 df-f1o 5086 |
This theorem is referenced by: f1o2d 5927 negf1o 8057 negiso 8617 iccf1o 9674 xrnegiso 10917 |
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