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Theorem unab 3601
 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 2142 . . 3
2 df-clab 2423 . . 3
3 df-clab 2423 . . . 4
4 df-clab 2423 . . . 4
53, 4orbi12i 508 . . 3
61, 2, 53bitr4ri 270 . 2
76uneqri 3482 1
 Colors of variables: wff set class Syntax hints:   wo 358   wceq 1652  wsb 1658   wcel 1725  cab 2422   cun 3311 This theorem is referenced by:  unrab  3605  rabun2  3613  dfif6  3735  unopab  4277  dmun  5069  hashf1lem2  11698  vdwlem6  13347  vdgrun  21665  vdgrfiun  21666  diophun  26824 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 2951  df-un 3318
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