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Theorem unass 3233
 Description: Associative law for union of classes. Exercise 8 of [TakeutiZaring] p. 17. (Contributed by NM, 3-May-1994.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
unass

Proof of Theorem unass
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elun 3217 . . 3
2 elun 3217 . . . 4
32orbi2i 751 . . 3
4 elun 3217 . . . . 5
54orbi1i 752 . . . 4
6 orass 756 . . . 4
75, 6bitr2i 184 . . 3
81, 3, 73bitrri 206 . 2
98uneqri 3218 1
 Colors of variables: wff set class Syntax hints:   wo 697   wceq 1331   wcel 1480   cun 3069 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075 This theorem is referenced by:  un12  3234  un23  3235  un4  3236  qdass  3620  qdassr  3621  rdgisucinc  6282  oasuc  6360  unfidisj  6810  undifdc  6812  djuassen  7073  fzosplitprm1  10011  hashunlem  10550
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