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Mirrors > Home > ILE Home > Th. List > dfoprab2 | Unicode version |
Description: Class abstraction for operations in terms of class abstraction of ordered pairs. (Contributed by NM, 12-Mar-1995.) |
Ref | Expression |
---|---|
dfoprab2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom 1641 |
. . . 4
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2 | exrot4 1668 |
. . . . 5
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3 | opeq1 3737 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 3 | eqeq2d 2166 |
. . . . . . . . . . 11
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5 | 4 | pm5.32ri 451 |
. . . . . . . . . 10
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6 | 5 | anbi1i 454 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | anass 399 |
. . . . . . . . 9
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8 | an32 552 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | 6, 7, 8 | 3bitr3i 209 |
. . . . . . . 8
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10 | 9 | exbii 1582 |
. . . . . . 7
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11 | vex 2712 |
. . . . . . . . . 10
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12 | vex 2712 |
. . . . . . . . . 10
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13 | 11, 12 | opex 4184 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | 13 | isseti 2717 |
. . . . . . . 8
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15 | 19.42v 1883 |
. . . . . . . 8
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16 | 14, 15 | mpbiran2 926 |
. . . . . . 7
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17 | 10, 16 | bitri 183 |
. . . . . 6
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18 | 17 | 3exbii 1584 |
. . . . 5
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19 | 2, 18 | bitri 183 |
. . . 4
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20 | 19.42vv 1888 |
. . . . 5
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21 | 20 | 2exbii 1583 |
. . . 4
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22 | 1, 19, 21 | 3bitr3i 209 |
. . 3
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23 | 22 | abbii 2270 |
. 2
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24 | df-oprab 5818 |
. 2
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25 | df-opab 4022 |
. 2
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26 | 23, 24, 25 | 3eqtr4i 2185 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1481 ax-10 1482 ax-11 1483 ax-i12 1484 ax-bndl 1486 ax-4 1487 ax-17 1503 ax-i9 1507 ax-ial 1511 ax-i5r 1512 ax-14 2128 ax-ext 2136 ax-sep 4078 ax-pow 4130 ax-pr 4164 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1740 df-clab 2141 df-cleq 2147 df-clel 2150 df-nfc 2285 df-v 2711 df-un 3102 df-in 3104 df-ss 3111 df-pw 3541 df-sn 3562 df-pr 3563 df-op 3565 df-opab 4022 df-oprab 5818 |
This theorem is referenced by: reloprab 5859 cbvoprab1 5883 cbvoprab12 5885 cbvoprab3 5887 dmoprab 5892 rnoprab 5894 ssoprab2i 5900 mpomptx 5902 resoprab 5907 funoprabg 5910 ov6g 5948 dfoprab3s 6128 xpcomco 6760 |
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