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Mirrors > Home > ILE Home > Th. List > tposoprab | Unicode version |
Description: Transposition of a class of ordered triples. (Contributed by Mario Carneiro, 10-Sep-2015.) |
Ref | Expression |
---|---|
tposoprab.1 |
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Ref | Expression |
---|---|
tposoprab |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tposoprab.1 |
. . 3
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2 | 1 | tposeqi 6128 |
. 2
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3 | reldmoprab 5810 |
. . 3
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4 | dftpos3 6113 |
. . 3
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5 | 3, 4 | ax-mp 7 |
. 2
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6 | nfcv 2255 |
. . . . 5
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7 | nfoprab2 5775 |
. . . . 5
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8 | nfcv 2255 |
. . . . 5
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9 | 6, 7, 8 | nfbr 3939 |
. . . 4
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10 | nfcv 2255 |
. . . . 5
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11 | nfoprab1 5774 |
. . . . 5
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12 | nfcv 2255 |
. . . . 5
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13 | 10, 11, 12 | nfbr 3939 |
. . . 4
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14 | nfv 1491 |
. . . 4
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15 | nfv 1491 |
. . . 4
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16 | opeq12 3673 |
. . . . . 6
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17 | 16 | ancoms 266 |
. . . . 5
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18 | 17 | breq1d 3905 |
. . . 4
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19 | 9, 13, 14, 15, 18 | cbvoprab12 5799 |
. . 3
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20 | nfcv 2255 |
. . . . 5
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21 | nfoprab3 5776 |
. . . . 5
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22 | nfcv 2255 |
. . . . 5
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23 | 20, 21, 22 | nfbr 3939 |
. . . 4
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24 | nfv 1491 |
. . . 4
![]() ![]() ![]() ![]() | |
25 | breq2 3899 |
. . . . 5
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26 | df-br 3896 |
. . . . . 6
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27 | oprabid 5757 |
. . . . . 6
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28 | 26, 27 | bitri 183 |
. . . . 5
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29 | 25, 28 | syl6bb 195 |
. . . 4
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30 | 23, 24, 29 | cbvoprab3 5801 |
. . 3
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31 | 19, 30 | eqtri 2135 |
. 2
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32 | 2, 5, 31 | 3eqtri 2139 |
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-in1 586 ax-in2 587 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-13 1474 ax-14 1475 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 ax-sep 4006 ax-nul 4014 ax-pow 4058 ax-pr 4091 ax-un 4315 ax-setind 4412 |
This theorem depends on definitions: df-bi 116 df-3an 947 df-tru 1317 df-fal 1320 df-nf 1420 df-sb 1719 df-eu 1978 df-mo 1979 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-ne 2283 df-ral 2395 df-rex 2396 df-rab 2399 df-v 2659 df-sbc 2879 df-dif 3039 df-un 3041 df-in 3043 df-ss 3050 df-nul 3330 df-pw 3478 df-sn 3499 df-pr 3500 df-op 3502 df-uni 3703 df-br 3896 df-opab 3950 df-mpt 3951 df-id 4175 df-xp 4505 df-rel 4506 df-cnv 4507 df-co 4508 df-dm 4509 df-rn 4510 df-res 4511 df-ima 4512 df-iota 5046 df-fun 5083 df-fn 5084 df-fv 5089 df-oprab 5732 df-tpos 6096 |
This theorem is referenced by: tposmpo 6132 |
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