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Theorem coundir 5372
 Description: Class composition distributes over union. (Contributed by NM, 21-Dec-2008.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Assertion
Ref Expression
coundir

Proof of Theorem coundir
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 unopab 4284 . . 3
2 brun 4258 . . . . . . . 8
32anbi2i 676 . . . . . . 7
4 andi 838 . . . . . . 7
53, 4bitri 241 . . . . . 6
65exbii 1592 . . . . 5
7 19.43 1615 . . . . 5
86, 7bitr2i 242 . . . 4
98opabbii 4272 . . 3
101, 9eqtri 2456 . 2
11 df-co 4887 . . 3
12 df-co 4887 . . 3
1311, 12uneq12i 3499 . 2
14 df-co 4887 . 2
1510, 13, 143eqtr4ri 2467 1
 Colors of variables: wff set class Syntax hints:   wo 358   wa 359  wex 1550   wceq 1652   cun 3318   class class class wbr 4212  copab 4265   ccom 4882 This theorem is referenced by:  diophrw  26817  diophren  26874 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 2417 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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-un 3325  df-br 4213  df-opab 4267  df-co 4887
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