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Theorem equncom 3428
Description: If a class equals the union of two other classes, then it equals the union of those two classes commuted. equncom 3428 was automatically derived from equncomVD 28314 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 3427 . 2  |-  ( B  u.  C )  =  ( C  u.  B
)
21eqeq2i 2390 1  |-  ( A  =  ( B  u.  C )  <->  A  =  ( C  u.  B
) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    = wceq 1649    u. cun 3254
This theorem is referenced by:  equncomi  3429  equncomiVD  28315
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-v 2894  df-un 3261
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