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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 1642 | . . . 4 | |
2 | exrot4 1669 | . . . . 5 | |
3 | opeq1 3705 | . . . . . . . . . . . 12 | |
4 | 3 | eqeq2d 2151 | . . . . . . . . . . 11 |
5 | 4 | pm5.32ri 450 | . . . . . . . . . 10 |
6 | 5 | anbi1i 453 | . . . . . . . . 9 |
7 | anass 398 | . . . . . . . . 9 | |
8 | an32 551 | . . . . . . . . 9 | |
9 | 6, 7, 8 | 3bitr3i 209 | . . . . . . . 8 |
10 | 9 | exbii 1584 | . . . . . . 7 |
11 | vex 2689 | . . . . . . . . . 10 | |
12 | vex 2689 | . . . . . . . . . 10 | |
13 | 11, 12 | opex 4151 | . . . . . . . . 9 |
14 | 13 | isseti 2694 | . . . . . . . 8 |
15 | 19.42v 1878 | . . . . . . . 8 | |
16 | 14, 15 | mpbiran2 925 | . . . . . . 7 |
17 | 10, 16 | bitri 183 | . . . . . 6 |
18 | 17 | 3exbii 1586 | . . . . 5 |
19 | 2, 18 | bitri 183 | . . . 4 |
20 | 19.42vv 1883 | . . . . 5 | |
21 | 20 | 2exbii 1585 | . . . 4 |
22 | 1, 19, 21 | 3bitr3i 209 | . . 3 |
23 | 22 | abbii 2255 | . 2 |
24 | df-oprab 5778 | . 2 | |
25 | df-opab 3990 | . 2 | |
26 | 23, 24, 25 | 3eqtr4i 2170 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1331 wex 1468 cab 2125 cop 3530 copab 3988 coprab 5775 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-opab 3990 df-oprab 5778 |
This theorem is referenced by: reloprab 5819 cbvoprab1 5843 cbvoprab12 5845 cbvoprab3 5847 dmoprab 5852 rnoprab 5854 ssoprab2i 5860 mpomptx 5862 resoprab 5867 funoprabg 5870 ov6g 5908 dfoprab3s 6088 xpcomco 6720 |
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