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Theorem unab 3764
Description: Union of two class abstractions. (Contributed by NM, 29-Sep-2002.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
unab

Proof of Theorem unab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbor 2139 . . 3
2 df-clab 2443 . . 3
3 df-clab 2443 . . . 4
4 df-clab 2443 . . . 4
53, 4orbi12i 521 . . 3
61, 2, 53bitr4ri 278 . 2
76uneqri 3645 1
Colors of variables: wff setvar class
Syntax hints:  \/wo 368  =wceq 1395  [wsb 1739  e.wcel 1818  {cab 2442  u.cun 3473
This theorem is referenced by:  unrab  3768  rabun2  3776  dfif6  3944  unopab  4527  dmun  5214  hashf1lem2  12505  vdwlem6  14504  vdgrun  24901  vdgrfiun  24902  diophun  30707
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3480
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