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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 1554 | . . . 4 | |
2 | exrot4 1581 | . . . . 5 | |
3 | opeq1 3549 | . . . . . . . . . . . 12 | |
4 | 3 | eqeq2d 2051 | . . . . . . . . . . 11 |
5 | 4 | pm5.32ri 428 | . . . . . . . . . 10 |
6 | 5 | anbi1i 431 | . . . . . . . . 9 |
7 | anass 381 | . . . . . . . . 9 | |
8 | an32 496 | . . . . . . . . 9 | |
9 | 6, 7, 8 | 3bitr3i 199 | . . . . . . . 8 |
10 | 9 | exbii 1496 | . . . . . . 7 |
11 | vex 2560 | . . . . . . . . . 10 | |
12 | vex 2560 | . . . . . . . . . 10 | |
13 | 11, 12 | opex 3966 | . . . . . . . . 9 |
14 | 13 | isseti 2563 | . . . . . . . 8 |
15 | 19.42v 1786 | . . . . . . . 8 | |
16 | 14, 15 | mpbiran2 848 | . . . . . . 7 |
17 | 10, 16 | bitri 173 | . . . . . 6 |
18 | 17 | 3exbii 1498 | . . . . 5 |
19 | 2, 18 | bitri 173 | . . . 4 |
20 | 19.42vv 1788 | . . . . 5 | |
21 | 20 | 2exbii 1497 | . . . 4 |
22 | 1, 19, 21 | 3bitr3i 199 | . . 3 |
23 | 22 | abbii 2153 | . 2 |
24 | df-oprab 5516 | . 2 | |
25 | df-opab 3819 | . 2 | |
26 | 23, 24, 25 | 3eqtr4i 2070 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wceq 1243 wex 1381 cab 2026 cop 3378 copab 3817 coprab 5513 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-opab 3819 df-oprab 5516 |
This theorem is referenced by: reloprab 5553 cbvoprab1 5576 cbvoprab12 5578 cbvoprab3 5580 dmoprab 5585 rnoprab 5587 ssoprab2i 5593 mpt2mptx 5595 resoprab 5597 funoprabg 5600 ov6g 5638 dfoprab3s 5816 xpcomco 6300 |
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