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Theorem uncom 3064
Description: Commutative law for union of classes. Exercise 6 of [TakeutiZaring] p. 17. (Contributed by NM, 25-Jun-1998.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
uncom  u.  u.

Proof of Theorem uncom
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 orcom 634 . . 3
2 elun 3061 . . 3  u.
31, 2bitr4i 176 . 2  u.
43uneqri 3062 1  u.  u.
Colors of variables: wff set class
Syntax hints:   wo 616   wceq 1228   wcel 1374    u. cun 2892
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537  df-un 2899
This theorem is referenced by:  equncom  3065  uneq2  3068  un12  3078  un23  3079  ssun2  3084  unss2  3091  ssequn2  3093  undir  3164  dif32  3177  disjpss  3255  undif2ss  3276  uneqdifeqim  3285  prcom  3420  tpass  3440  prprc1  3452  difsnss  3484  suc0  4097  fvun2  5165  fmptpr  5280  fvsnun2  5286  fsnunfv  5288  omv2  5960
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