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Theorem uneq2 3438
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 3437 . 2  |-  ( A  =  B  ->  ( A  u.  C )  =  ( B  u.  C ) )
2 uncom 3434 . 2  |-  ( C  u.  A )  =  ( A  u.  C
)
3 uncom 3434 . 2  |-  ( C  u.  B )  =  ( B  u.  C
)
41, 2, 33eqtr4g 2444 1  |-  ( A  =  B  ->  ( C  u.  A )  =  ( C  u.  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649    u. cun 3261
This theorem is referenced by:  uneq12  3439  uneq2i  3441  uneq2d  3444  uneqin  3535  disjssun  3628  uniprg  3972  sucprc  4597  unexb  4649  undifixp  7034  unxpdom  7252  ackbij1lem16  8048  fin23lem28  8153  ttukeylem6  8327  ipodrsima  14518  mplsubglem  16425  mretopd  17079  iscldtop  17082  dfcon2  17403  nconsubb  17407  spanun  22895  nofulllem1  25380  brsuccf  25504  rankung  25821  comppfsc  26078  nacsfix  26457  eldioph4b  26563  eldioph4i  26564  fiuneneq  27182  paddval  29912  dochsatshp  31566
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 2368
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 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-v 2901  df-un 3268
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