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Theorem coundi 5363
 Description: Class composition distributes over union. (Contributed by NM, 21-Dec-2008.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Assertion
Ref Expression
coundi

Proof of Theorem coundi
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 unopab 4276 . . 3
2 brun 4250 . . . . . . . 8
32anbi1i 677 . . . . . . 7
4 andir 839 . . . . . . 7
53, 4bitri 241 . . . . . 6
65exbii 1592 . . . . 5
7 19.43 1615 . . . . 5
86, 7bitr2i 242 . . . 4
98opabbii 4264 . . 3
101, 9eqtri 2455 . 2
11 df-co 4879 . . 3
12 df-co 4879 . . 3
1311, 12uneq12i 3491 . 2
14 df-co 4879 . 2
1510, 13, 143eqtr4ri 2466 1
 Colors of variables: wff set class Syntax hints:   wo 358   wa 359  wex 1550   wceq 1652   cun 3310   class class class wbr 4204  copab 4257   ccom 4874 This theorem is referenced by:  relcoi1  5390  ustssco  18236  cvmliftlem10  24973  diophren  26865  mvdco  27356 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-un 3317  df-br 4205  df-opab 4259  df-co 4879
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