Theorem equncom 3304

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 3303	. 2 |- ( B u. C ) = ( C u. B )
2	1	eqeq2i 2204	1 |- ( A = ( B u. C ) <-> A = ( C u. B ) )

Syntax hints:   <-> wb 105   = wceq 1364   u. cun 3151

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-un 3157

This theorem is referenced by:  equncomi  3305