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Theorem equncom 3088
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
StepHypRef Expression
1 uncom 3087 . 2  |-  ( B  u.  C )  =  ( C  u.  B
)
21eqeq2i 2050 1  |-  ( A  =  ( B  u.  C )  <->  A  =  ( C  u.  B
) )
Colors of variables: wff set class
Syntax hints:    <-> wb 98    = wceq 1243    u. cun 2915
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922
This theorem is referenced by:  equncomi  3089
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