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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 3338 | . . 3 | |
2 | 19.43 1607 | . . . . 5 | |
3 | andi 807 | . . . . . . . 8 | |
4 | 3 | exbii 1584 | . . . . . . 7 |
5 | 19.43 1607 | . . . . . . 7 | |
6 | 4, 5 | bitr2i 184 | . . . . . 6 |
7 | 6 | exbii 1584 | . . . . 5 |
8 | 2, 7 | bitr3i 185 | . . . 4 |
9 | 8 | abbii 2253 | . . 3 |
10 | 1, 9 | eqtri 2158 | . 2 |
11 | df-opab 3985 | . . 3 | |
12 | df-opab 3985 | . . 3 | |
13 | 11, 12 | uneq12i 3223 | . 2 |
14 | df-opab 3985 | . 2 | |
15 | 10, 13, 14 | 3eqtr4i 2168 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wo 697 wceq 1331 wex 1468 cab 2123 cun 3064 cop 3525 copab 3983 |
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-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-opab 3985 |
This theorem is referenced by: xpundi 4590 xpundir 4591 cnvun 4939 coundi 5035 coundir 5036 mptun 5249 |
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