Theorem equncom 3117

Description: If a class equals the union of two other classes, then it equals the union of those two classes commuted. (Contributed by Alan Sare, 18-Feb-2012.)

Assertion

Ref	Expression
equncom	|- ( A = ( B u. C ) <-> A = ( C u. B ) )

Proof of Theorem equncom

Step	Hyp	Ref	Expression
1		uncom 3116	. 2 |- ( B u. C ) = ( C u. B )
2	1	eqeq2i 2091	1 |- ( A = ( B u. C ) <-> A = ( C u. B ) )

Syntax hints:   <-> wb 103   = wceq 1284   u. cun 2971

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-v 2603  df-un 2977

This theorem is referenced by:  equncomi  3118