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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 5974 |
. 2
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3 | reldmoprab 5668 |
. . 3
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4 | dftpos3 5959 |
. . 3
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5 | 3, 4 | ax-mp 7 |
. 2
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6 | nfcv 2223 |
. . . . 5
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7 | nfoprab2 5634 |
. . . . 5
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8 | nfcv 2223 |
. . . . 5
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9 | 6, 7, 8 | nfbr 3855 |
. . . 4
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10 | nfcv 2223 |
. . . . 5
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11 | nfoprab1 5633 |
. . . . 5
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12 | nfcv 2223 |
. . . . 5
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13 | 10, 11, 12 | nfbr 3855 |
. . . 4
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14 | nfv 1462 |
. . . 4
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15 | nfv 1462 |
. . . 4
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16 | opeq12 3598 |
. . . . . 6
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17 | 16 | ancoms 264 |
. . . . 5
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18 | 17 | breq1d 3821 |
. . . 4
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19 | 9, 13, 14, 15, 18 | cbvoprab12 5657 |
. . 3
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20 | nfcv 2223 |
. . . . 5
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21 | nfoprab3 5635 |
. . . . 5
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22 | nfcv 2223 |
. . . . 5
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23 | 20, 21, 22 | nfbr 3855 |
. . . 4
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24 | nfv 1462 |
. . . 4
![]() ![]() ![]() ![]() | |
25 | breq2 3815 |
. . . . 5
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26 | df-br 3812 |
. . . . . 6
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27 | oprabid 5616 |
. . . . . 6
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28 | 26, 27 | bitri 182 |
. . . . 5
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29 | 25, 28 | syl6bb 194 |
. . . 4
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30 | 23, 24, 29 | cbvoprab3 5659 |
. . 3
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31 | 19, 30 | eqtri 2103 |
. 2
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32 | 2, 5, 31 | 3eqtri 2107 |
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-in1 577 ax-in2 578 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-13 1445 ax-14 1446 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 ax-sep 3922 ax-nul 3930 ax-pow 3974 ax-pr 4000 ax-un 4224 ax-setind 4316 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-fal 1291 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-ne 2250 df-ral 2358 df-rex 2359 df-rab 2362 df-v 2614 df-sbc 2827 df-dif 2986 df-un 2988 df-in 2990 df-ss 2997 df-nul 3270 df-pw 3408 df-sn 3428 df-pr 3429 df-op 3431 df-uni 3628 df-br 3812 df-opab 3866 df-mpt 3867 df-id 4084 df-xp 4407 df-rel 4408 df-cnv 4409 df-co 4410 df-dm 4411 df-rn 4412 df-res 4413 df-ima 4414 df-iota 4934 df-fun 4971 df-fn 4972 df-fv 4977 df-oprab 5595 df-tpos 5942 |
This theorem is referenced by: tposmpt2 5978 |
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