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Theorem equncom 3484
Description: If a class equals the union of two other classes, then it equals the union of those two classes commuted. equncom 3484 was automatically derived from equncomVD 28917 using the tools program translatewithout_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
StepHypRef Expression
1 uncom 3483 . 2  |-  ( B  u.  C )  =  ( C  u.  B
)
21eqeq2i 2445 1  |-  ( A  =  ( B  u.  C )  <->  A  =  ( C  u.  B
) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    = wceq 1652    u. cun 3310
This theorem is referenced by:  equncomi  3485  equncomiVD  28918
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-un 3317
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