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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom 1651 | . . . 4 | |
2 | exrot4 1678 | . . . . 5 | |
3 | opeq1 3752 | . . . . . . . . . . . 12 | |
4 | 3 | eqeq2d 2176 | . . . . . . . . . . 11 |
5 | 4 | pm5.32ri 451 | . . . . . . . . . 10 |
6 | 5 | anbi1i 454 | . . . . . . . . 9 |
7 | anass 399 | . . . . . . . . 9 | |
8 | an32 552 | . . . . . . . . 9 | |
9 | 6, 7, 8 | 3bitr3i 209 | . . . . . . . 8 |
10 | 9 | exbii 1592 | . . . . . . 7 |
11 | vex 2724 | . . . . . . . . . 10 | |
12 | vex 2724 | . . . . . . . . . 10 | |
13 | 11, 12 | opex 4201 | . . . . . . . . 9 |
14 | 13 | isseti 2729 | . . . . . . . 8 |
15 | 19.42v 1893 | . . . . . . . 8 | |
16 | 14, 15 | mpbiran2 930 | . . . . . . 7 |
17 | 10, 16 | bitri 183 | . . . . . 6 |
18 | 17 | 3exbii 1594 | . . . . 5 |
19 | 2, 18 | bitri 183 | . . . 4 |
20 | 19.42vv 1898 | . . . . 5 | |
21 | 20 | 2exbii 1593 | . . . 4 |
22 | 1, 19, 21 | 3bitr3i 209 | . . 3 |
23 | 22 | abbii 2280 | . 2 |
24 | df-oprab 5840 | . 2 | |
25 | df-opab 4038 | . 2 | |
26 | 23, 24, 25 | 3eqtr4i 2195 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1342 wex 1479 cab 2150 cop 3573 copab 4036 coprab 5837 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-opab 4038 df-oprab 5840 |
This theorem is referenced by: reloprab 5881 cbvoprab1 5905 cbvoprab12 5907 cbvoprab3 5909 dmoprab 5914 rnoprab 5916 ssoprab2i 5922 mpomptx 5924 resoprab 5929 funoprabg 5932 ov6g 5970 dfoprab3s 6150 xpcomco 6783 |
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