Theorem equncom 3648

Description: If a class equals the union of two other classes, then it equals the union of those two classes commuted. equncom 3648 was automatically derived from equncomVD 33668 using the tools program translate_without_overwriting.cmd and minimizing. (Contributed by Alan Sare, 18-Feb-2012.)

Assertion

Ref	Expression
equncom

Proof of Theorem equncom

Step	Hyp	Ref	Expression
1		uncom 3647	. 2
2	1	eqeq2i 2475	1

Syntax hints:  <->wb 184  =wceq 1395  u.cun 3473

This theorem is referenced by:  equncomi  3649  equncomiVD  33669

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