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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 3204 | . . 3 | |
2 | 19.43 1519 | . . . . 5 | |
3 | andi 731 | . . . . . . . 8 | |
4 | 3 | exbii 1496 | . . . . . . 7 |
5 | 19.43 1519 | . . . . . . 7 | |
6 | 4, 5 | bitr2i 174 | . . . . . 6 |
7 | 6 | exbii 1496 | . . . . 5 |
8 | 2, 7 | bitr3i 175 | . . . 4 |
9 | 8 | abbii 2153 | . . 3 |
10 | 1, 9 | eqtri 2060 | . 2 |
11 | df-opab 3819 | . . 3 | |
12 | df-opab 3819 | . . 3 | |
13 | 11, 12 | uneq12i 3095 | . 2 |
14 | df-opab 3819 | . 2 | |
15 | 10, 13, 14 | 3eqtr4i 2070 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wo 629 wceq 1243 wex 1381 cab 2026 cun 2915 cop 3378 copab 3817 |
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-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 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-opab 3819 |
This theorem is referenced by: xpundi 4396 xpundir 4397 cnvun 4729 coundi 4822 coundir 4823 mptun 5029 |
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