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Mirrors > Home > ILE Home > Th. List > unopab | Unicode version |
Description: Union of two ordered pair class abstractions. (Contributed by NM, 30-Sep-2002.) |
Ref | Expression |
---|---|
unopab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unab 3384 | . . 3 | |
2 | 19.43 1615 | . . . . 5 | |
3 | andi 808 | . . . . . . . 8 | |
4 | 3 | exbii 1592 | . . . . . . 7 |
5 | 19.43 1615 | . . . . . . 7 | |
6 | 4, 5 | bitr2i 184 | . . . . . 6 |
7 | 6 | exbii 1592 | . . . . 5 |
8 | 2, 7 | bitr3i 185 | . . . 4 |
9 | 8 | abbii 2280 | . . 3 |
10 | 1, 9 | eqtri 2185 | . 2 |
11 | df-opab 4038 | . . 3 | |
12 | df-opab 4038 | . . 3 | |
13 | 11, 12 | uneq12i 3269 | . 2 |
14 | df-opab 4038 | . 2 | |
15 | 10, 13, 14 | 3eqtr4i 2195 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wo 698 wceq 1342 wex 1479 cab 2150 cun 3109 cop 3573 copab 4036 |
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-ext 2146 |
This theorem depends on definitions: df-bi 116 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-opab 4038 |
This theorem is referenced by: xpundi 4654 xpundir 4655 cnvun 5003 coundi 5099 coundir 5100 mptun 5313 |
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