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Theorem equncom 3320
Description: If a class equals the union of two other classes, then it equals the union of those two classes commuted. equncom 3320 was automatically derived from equncomVD 28644 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 3319 . 2  |-  ( B  u.  C )  =  ( C  u.  B
)
21eqeq2i 2293 1  |-  ( A  =  ( B  u.  C )  <->  A  =  ( C  u.  B
) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    = wceq 1623    u. cun 3150
This theorem is referenced by:  equncomi  3321  splint  25048  equncomiVD  28645
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-un 3157
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