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Theorem uneq2 3455
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 3454 . 2  |-  ( A  =  B  ->  ( A  u.  C )  =  ( B  u.  C ) )
2 uncom 3451 . 2  |-  ( C  u.  A )  =  ( A  u.  C
)
3 uncom 3451 . 2  |-  ( C  u.  B )  =  ( B  u.  C
)
41, 2, 33eqtr4g 2461 1  |-  ( A  =  B  ->  ( C  u.  A )  =  ( C  u.  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649    u. cun 3278
This theorem is referenced by:  uneq12  3456  uneq2i  3458  uneq2d  3461  uneqin  3552  disjssun  3645  uniprg  3990  sucprc  4616  unexb  4668  undifixp  7057  unxpdom  7275  ackbij1lem16  8071  fin23lem28  8176  ttukeylem6  8350  ipodrsima  14546  mplsubglem  16453  mretopd  17111  iscldtop  17114  dfcon2  17435  nconsubb  17439  spanun  23000  nofulllem1  25570  brsuccf  25694  rankung  26011  comppfsc  26277  nacsfix  26656  eldioph4b  26762  eldioph4i  26763  fiuneneq  27381  paddval  30280  dochsatshp  31934
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 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
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 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-v 2918  df-un 3285
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