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Theorem uneq2 3487
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 3486 . 2  |-  ( A  =  B  ->  ( A  u.  C )  =  ( B  u.  C ) )
2 uncom 3483 . 2  |-  ( C  u.  A )  =  ( A  u.  C
)
3 uncom 3483 . 2  |-  ( C  u.  B )  =  ( B  u.  C
)
41, 2, 33eqtr4g 2492 1  |-  ( A  =  B  ->  ( C  u.  A )  =  ( C  u.  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652    u. cun 3310
This theorem is referenced by:  uneq12  3488  uneq2i  3490  uneq2d  3493  uneqin  3584  disjssun  3677  uniprg  4022  sucprc  4648  unexb  4701  undifixp  7090  unxpdom  7308  ackbij1lem16  8107  fin23lem28  8212  ttukeylem6  8386  ipodrsima  14583  mplsubglem  16490  mretopd  17148  iscldtop  17151  dfcon2  17474  nconsubb  17478  spanun  23039  nofulllem1  25649  brsuccf  25778  rankung  26099  comppfsc  26378  nacsfix  26757  eldioph4b  26863  eldioph4i  26864  fiuneneq  27481  paddval  30532  dochsatshp  32186
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-un 3317
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