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Theorem uneq2 3488
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 3487 . 2  |-  ( A  =  B  ->  ( A  u.  C )  =  ( B  u.  C ) )
2 uncom 3484 . 2  |-  ( C  u.  A )  =  ( A  u.  C
)
3 uncom 3484 . 2  |-  ( C  u.  B )  =  ( B  u.  C
)
41, 2, 33eqtr4g 2493 1  |-  ( A  =  B  ->  ( C  u.  A )  =  ( C  u.  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652    u. cun 3311
This theorem is referenced by:  uneq12  3489  uneq2i  3491  uneq2d  3494  uneqin  3585  disjssun  3678  uniprg  4023  sucprc  4649  unexb  4702  undifixp  7091  unxpdom  7309  ackbij1lem16  8108  fin23lem28  8213  ttukeylem6  8387  ipodrsima  14584  mplsubglem  16491  mretopd  17149  iscldtop  17152  dfcon2  17475  nconsubb  17479  spanun  23040  nofulllem1  25650  brsuccf  25779  rankung  26100  comppfsc  26379  nacsfix  26758  eldioph4b  26864  eldioph4i  26865  fiuneneq  27482  paddval  30533  dochsatshp  32187
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 2417
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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2951  df-un 3318
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