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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 2154 |
. . . . . 6
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5 | 2, 4 | syl 14 |
. . . . 5
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6 | 5 | impr 371 |
. . . 4
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7 | f1o2d.4 |
. . . . . . . 8
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8 | 7 | biimpar 291 |
. . . . . . 7
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9 | 8 | exp42 363 |
. . . . . 6
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10 | 9 | com34 82 |
. . . . 5
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11 | 10 | imp32 253 |
. . . 4
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12 | 6, 11 | jcai 304 |
. . 3
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13 | eleq1a 2154 |
. . . . . 6
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14 | 3, 13 | syl 14 |
. . . . 5
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15 | 14 | impr 371 |
. . . 4
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16 | 7 | biimpa 290 |
. . . . . . . 8
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17 | 16 | exp42 363 |
. . . . . . 7
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18 | 17 | com23 77 |
. . . . . 6
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19 | 18 | com34 82 |
. . . . 5
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20 | 19 | imp32 253 |
. . . 4
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21 | 15, 20 | jcai 304 |
. . 3
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22 | 12, 21 | impbida 561 |
. 2
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23 | 1, 2, 3, 22 | f1ocnvd 5779 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-14 1446 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 ax-sep 3922 ax-pow 3974 ax-pr 3999 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-nf 1391 df-sb 1688 df-eu 1946 df-mo 1947 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-ral 2358 df-rex 2359 df-v 2614 df-un 2988 df-in 2990 df-ss 2997 df-pw 3408 df-sn 3428 df-pr 3429 df-op 3431 df-br 3812 df-opab 3866 df-mpt 3867 df-id 4083 df-xp 4405 df-rel 4406 df-cnv 4407 df-co 4408 df-dm 4409 df-rn 4410 df-fun 4969 df-fn 4970 df-f 4971 df-f1 4972 df-fo 4973 df-f1o 4974 |
This theorem is referenced by: f1o2d 5782 negf1o 7761 negiso 8308 iccf1o 9314 |
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