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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 6291 |
. 2
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3 | reldmoprab 5973 |
. . 3
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4 | dftpos3 6276 |
. . 3
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5 | 3, 4 | ax-mp 5 |
. 2
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6 | nfcv 2329 |
. . . . 5
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7 | nfoprab2 5938 |
. . . . 5
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8 | nfcv 2329 |
. . . . 5
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9 | 6, 7, 8 | nfbr 4061 |
. . . 4
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10 | nfcv 2329 |
. . . . 5
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11 | nfoprab1 5937 |
. . . . 5
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12 | nfcv 2329 |
. . . . 5
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13 | 10, 11, 12 | nfbr 4061 |
. . . 4
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14 | nfv 1538 |
. . . 4
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15 | nfv 1538 |
. . . 4
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16 | opeq12 3792 |
. . . . . 6
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17 | 16 | ancoms 268 |
. . . . 5
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18 | 17 | breq1d 4025 |
. . . 4
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19 | 9, 13, 14, 15, 18 | cbvoprab12 5962 |
. . 3
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20 | nfcv 2329 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
21 | nfoprab3 5939 |
. . . . 5
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22 | nfcv 2329 |
. . . . 5
![]() ![]() ![]() ![]() | |
23 | 20, 21, 22 | nfbr 4061 |
. . . 4
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24 | nfv 1538 |
. . . 4
![]() ![]() ![]() ![]() | |
25 | breq2 4019 |
. . . . 5
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26 | df-br 4016 |
. . . . . 6
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27 | oprabid 5920 |
. . . . . 6
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28 | 26, 27 | bitri 184 |
. . . . 5
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29 | 25, 28 | bitrdi 196 |
. . . 4
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30 | 23, 24, 29 | cbvoprab3 5964 |
. . 3
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31 | 19, 30 | eqtri 2208 |
. 2
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32 | 2, 5, 31 | 3eqtri 2212 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-13 2160 ax-14 2161 ax-ext 2169 ax-sep 4133 ax-nul 4141 ax-pow 4186 ax-pr 4221 ax-un 4445 ax-setind 4548 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-fal 1369 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ne 2358 df-ral 2470 df-rex 2471 df-rab 2474 df-v 2751 df-sbc 2975 df-dif 3143 df-un 3145 df-in 3147 df-ss 3154 df-nul 3435 df-pw 3589 df-sn 3610 df-pr 3611 df-op 3613 df-uni 3822 df-br 4016 df-opab 4077 df-mpt 4078 df-id 4305 df-xp 4644 df-rel 4645 df-cnv 4646 df-co 4647 df-dm 4648 df-rn 4649 df-res 4650 df-ima 4651 df-iota 5190 df-fun 5230 df-fn 5231 df-fv 5236 df-oprab 5892 df-tpos 6259 |
This theorem is referenced by: tposmpo 6295 |
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