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Mirrors > Home > ILE Home > Th. List > coundir | Unicode version |
Description: Class composition distributes over union. (Contributed by NM, 21-Dec-2008.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
coundir |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unopab 3977 | . . 3 | |
2 | brun 3949 | . . . . . . . 8 | |
3 | 2 | anbi2i 452 | . . . . . . 7 |
4 | andi 792 | . . . . . . 7 | |
5 | 3, 4 | bitri 183 | . . . . . 6 |
6 | 5 | exbii 1569 | . . . . 5 |
7 | 19.43 1592 | . . . . 5 | |
8 | 6, 7 | bitr2i 184 | . . . 4 |
9 | 8 | opabbii 3965 | . . 3 |
10 | 1, 9 | eqtri 2138 | . 2 |
11 | df-co 4518 | . . 3 | |
12 | df-co 4518 | . . 3 | |
13 | 11, 12 | uneq12i 3198 | . 2 |
14 | df-co 4518 | . 2 | |
15 | 10, 13, 14 | 3eqtr4ri 2149 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wo 682 wceq 1316 wex 1453 cun 3039 class class class wbr 3899 copab 3958 ccom 4513 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 df-br 3900 df-opab 3960 df-co 4518 |
This theorem is referenced by: (None) |
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