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Mirrors > Home > ILE Home > Th. List > coundi | Unicode version |
Description: Class composition distributes over union. (Contributed by NM, 21-Dec-2008.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
coundi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unopab 3836 | . . 3 | |
2 | brun 3810 | . . . . . . . 8 | |
3 | 2 | anbi1i 431 | . . . . . . 7 |
4 | andir 732 | . . . . . . 7 | |
5 | 3, 4 | bitri 173 | . . . . . 6 |
6 | 5 | exbii 1496 | . . . . 5 |
7 | 19.43 1519 | . . . . 5 | |
8 | 6, 7 | bitr2i 174 | . . . 4 |
9 | 8 | opabbii 3824 | . . 3 |
10 | 1, 9 | eqtri 2060 | . 2 |
11 | df-co 4354 | . . 3 | |
12 | df-co 4354 | . . 3 | |
13 | 11, 12 | uneq12i 3095 | . 2 |
14 | df-co 4354 | . 2 | |
15 | 10, 13, 14 | 3eqtr4ri 2071 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wo 629 wceq 1243 wex 1381 cun 2915 class class class wbr 3764 copab 3817 ccom 4349 |
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-br 3765 df-opab 3819 df-co 4354 |
This theorem is referenced by: relcoi1 4849 |
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