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Mirrors > Home > NFE 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 3521 | . . 3 | |
2 | 19.43 1605 | . . . . 5 | |
3 | andi 837 | . . . . . . . 8 | |
4 | 3 | exbii 1582 | . . . . . . 7 |
5 | 19.43 1605 | . . . . . . 7 | |
6 | 4, 5 | bitr2i 241 | . . . . . 6 |
7 | 6 | exbii 1582 | . . . . 5 |
8 | 2, 7 | bitr3i 242 | . . . 4 |
9 | 8 | abbii 2465 | . . 3 |
10 | 1, 9 | eqtri 2373 | . 2 |
11 | df-opab 4623 | . . 3 | |
12 | df-opab 4623 | . . 3 | |
13 | 11, 12 | uneq12i 3416 | . 2 |
14 | df-opab 4623 | . 2 | |
15 | 10, 13, 14 | 3eqtr4i 2383 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wo 357 wa 358 wex 1541 wceq 1642 cab 2339 cun 3207 cop 4561 copab 4622 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-un 3214 df-opab 4623 |
This theorem is referenced by: xpundi 4832 xpundir 4833 cnvun 5033 coundi 5082 coundir 5083 |
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