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Theorem uneq2 3440
Description: Equality theorem for the union of two classes. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
uneq2  |-  ( A  =  B  ->  ( C  u.  A )  =  ( C  u.  B ) )

Proof of Theorem uneq2
StepHypRef Expression
1 uneq1 3439 . 2  |-  ( A  =  B  ->  ( A  u.  C )  =  ( B  u.  C ) )
2 uncom 3436 . 2  |-  ( C  u.  A )  =  ( A  u.  C
)
3 uncom 3436 . 2  |-  ( C  u.  B )  =  ( B  u.  C
)
41, 2, 33eqtr4g 2446 1  |-  ( A  =  B  ->  ( C  u.  A )  =  ( C  u.  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649    u. cun 3263
This theorem is referenced by:  uneq12  3441  uneq2i  3443  uneq2d  3446  uneqin  3537  disjssun  3630  uniprg  3974  sucprc  4599  unexb  4651  undifixp  7036  unxpdom  7254  ackbij1lem16  8050  fin23lem28  8155  ttukeylem6  8329  ipodrsima  14520  mplsubglem  16427  mretopd  17081  iscldtop  17084  dfcon2  17405  nconsubb  17409  spanun  22897  nofulllem1  25382  brsuccf  25506  rankung  25823  comppfsc  26080  nacsfix  26459  eldioph4b  26565  eldioph4i  26566  fiuneneq  27184  paddval  29914  dochsatshp  31568
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 2370
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 2376  df-cleq 2382  df-clel 2385  df-nfc 2514  df-v 2903  df-un 3270
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