Theorem equncom 3758

Description: If a class equals the union of two other classes, then it equals the union of those two classes commuted. equncom 3758 was automatically derived from equncomVD 39104 using the tools program translate_without_overwriting.cmd and minimizing. (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 3757	. 2 |- ( B u. C ) = ( C u. B )
2	1	eqeq2i 2634	1 |- ( A = ( B u. C ) <-> A = ( C u. B ) )

Syntax hints:   <-> wb 196   = wceq 1483   u. cun 3572

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-un 3579

This theorem is referenced by:  equncomi  3759  equncomiVD  39105