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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 1643 |
. . . 4
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2 | exrot4 1670 |
. . . . 5
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3 | opeq1 3713 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 3 | eqeq2d 2152 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | 4 | pm5.32ri 451 |
. . . . . . . . . 10
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6 | 5 | anbi1i 454 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | anass 399 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | an32 552 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | 6, 7, 8 | 3bitr3i 209 |
. . . . . . . 8
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10 | 9 | exbii 1585 |
. . . . . . 7
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11 | vex 2692 |
. . . . . . . . . 10
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12 | vex 2692 |
. . . . . . . . . 10
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13 | 11, 12 | opex 4159 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | 13 | isseti 2697 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 19.42v 1879 |
. . . . . . . 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 1587 |
. . . . 5
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19 | 2, 18 | bitri 183 |
. . . 4
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20 | 19.42vv 1884 |
. . . . 5
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21 | 20 | 2exbii 1586 |
. . . 4
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22 | 1, 19, 21 | 3bitr3i 209 |
. . 3
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23 | 22 | abbii 2256 |
. 2
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24 | df-oprab 5786 |
. 2
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25 | df-opab 3998 |
. 2
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26 | 23, 24, 25 | 3eqtr4i 2171 |
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 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-opab 3998 df-oprab 5786 |
This theorem is referenced by: reloprab 5827 cbvoprab1 5851 cbvoprab12 5853 cbvoprab3 5855 dmoprab 5860 rnoprab 5862 ssoprab2i 5868 mpomptx 5870 resoprab 5875 funoprabg 5878 ov6g 5916 dfoprab3s 6096 xpcomco 6728 |
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