Theorem un12 3661

Description: A rearrangement of union. (Contributed by NM, 12-Aug-2004.)

Assertion

Ref	Expression
un12

Proof of Theorem un12

Step	Hyp	Ref	Expression
1		uncom 3647	. . 3
2	1	uneq1i 3653	. 2
3		unass 3660	. 2
4		unass 3660	. 2
5	2, 3, 4	3eqtr3i 2494	1

Syntax hints:  =wceq 1395  u.cun 3473

This theorem is referenced by:  un23  3662  un4  3663  fresaun  5761  reconnlem1  21331  asindmre  30102

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