Theorem unass 3660

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.

Step	Hyp	Ref	Expression
1		elun 3644	. . 3
2		elun 3644	. . . 4
3	2	orbi2i 519	. . 3
4		elun 3644	. . . . 5
5	4	orbi1i 520	. . . 4
6		orass 524	. . . 4
7	5, 6	bitr2i 250	. . 3
8	1, 3, 7	3bitrri 272	. 2
9	8	uneqri 3645	1

Syntax hints:  \/wo 368  =wceq 1395  e.wcel 1818  u.cun 3473

This theorem is referenced by:  un12  3661  un23  3662  un4  3663  dfif5  3957  qdass  4129  qdassr  4130  ssunpr  4192  oarec  7230  domunfican  7813  cdaassen  8583  prunioo  11678  ioojoin  11680  fzosplitprm1  11919  s4prop  12863  strlemor2  14725  strlemor3  14726  phlstr  14778  prdsvalstr  14850  mreexexlem2d  15042  mreexexlem4d  15044  ordtbas  19693  reconnlem1  21331  lhop  22417  plyun0  22594  ex-un  25145  ex-pw  25150  subfacp1lem1  28623  fzosplitpr  32342

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