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Theorem coundi 5082
 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.)
Assertion
Ref Expression
coundi

Proof of Theorem coundi
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 unopab 4638 . . 3
2 brun 4692 . . . . . . . 8
32anbi1i 676 . . . . . . 7
4 andir 838 . . . . . . 7
53, 4bitri 240 . . . . . 6
65exbii 1582 . . . . 5
7 19.43 1605 . . . . 5
86, 7bitr2i 241 . . . 4
98opabbii 4626 . . 3
101, 9eqtri 2373 . 2
11 df-co 4726 . . 3
12 df-co 4726 . . 3
1311, 12uneq12i 3416 . 2
14 df-co 4726 . 2
1510, 13, 143eqtr4ri 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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