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Mirrors > Home > NFE Home > Th. List > coundi | Unicode version |
Description: Class composition distributes over union. (The proof was shortened by Andrew Salmon, 27-Aug-2011.) (Contributed by set.mm contributors, 21-Dec-2008.) (Revised by set.mm contributors, 27-Aug-2011.) |
Ref | Expression |
---|---|
coundi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unopab 4638 | . . 3 | |
2 | brun 4692 | . . . . . . . 8 | |
3 | 2 | anbi1i 676 | . . . . . . 7 |
4 | andir 838 | . . . . . . 7 | |
5 | 3, 4 | bitri 240 | . . . . . 6 |
6 | 5 | exbii 1582 | . . . . 5 |
7 | 19.43 1605 | . . . . 5 | |
8 | 6, 7 | bitr2i 241 | . . . 4 |
9 | 8 | opabbii 4626 | . . 3 |
10 | 1, 9 | eqtri 2373 | . 2 |
11 | df-co 4726 | . . 3 | |
12 | df-co 4726 | . . 3 | |
13 | 11, 12 | uneq12i 3416 | . 2 |
14 | df-co 4726 | . 2 | |
15 | 10, 13, 14 | 3eqtr4ri 2384 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wo 357 wa 358 wex 1541 wceq 1642 cun 3207 copab 4622 class class class wbr 4639 ccom 4721 |
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 df-br 4640 df-co 4726 |
This theorem is referenced by: (None) |
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