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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 1594 | . . . 4 | |
2 | exrot4 1621 | . . . . 5 | |
3 | opeq1 3570 | . . . . . . . . . . . 12 | |
4 | 3 | eqeq2d 2092 | . . . . . . . . . . 11 |
5 | 4 | pm5.32ri 442 | . . . . . . . . . 10 |
6 | 5 | anbi1i 445 | . . . . . . . . 9 |
7 | anass 393 | . . . . . . . . 9 | |
8 | an32 526 | . . . . . . . . 9 | |
9 | 6, 7, 8 | 3bitr3i 208 | . . . . . . . 8 |
10 | 9 | exbii 1536 | . . . . . . 7 |
11 | vex 2604 | . . . . . . . . . 10 | |
12 | vex 2604 | . . . . . . . . . 10 | |
13 | 11, 12 | opex 3984 | . . . . . . . . 9 |
14 | 13 | isseti 2607 | . . . . . . . 8 |
15 | 19.42v 1827 | . . . . . . . 8 | |
16 | 14, 15 | mpbiran2 882 | . . . . . . 7 |
17 | 10, 16 | bitri 182 | . . . . . 6 |
18 | 17 | 3exbii 1538 | . . . . 5 |
19 | 2, 18 | bitri 182 | . . . 4 |
20 | 19.42vv 1829 | . . . . 5 | |
21 | 20 | 2exbii 1537 | . . . 4 |
22 | 1, 19, 21 | 3bitr3i 208 | . . 3 |
23 | 22 | abbii 2194 | . 2 |
24 | df-oprab 5536 | . 2 | |
25 | df-opab 3840 | . 2 | |
26 | 23, 24, 25 | 3eqtr4i 2111 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 102 wceq 1284 wex 1421 cab 2067 cop 3401 copab 3838 coprab 5533 |
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-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-opab 3840 df-oprab 5536 |
This theorem is referenced by: reloprab 5573 cbvoprab1 5596 cbvoprab12 5598 cbvoprab3 5600 dmoprab 5605 rnoprab 5607 ssoprab2i 5613 mpt2mptx 5615 resoprab 5617 funoprabg 5620 ov6g 5658 dfoprab3s 5836 xpcomco 6323 |
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