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Theorem uneq2 3233
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 3232 . 2  |-  ( A  =  B  ->  ( A  u.  C )  =  ( B  u.  C ) )
2 uncom 3229 . 2  |-  ( C  u.  A )  =  ( A  u.  C
)
3 uncom 3229 . 2  |-  ( C  u.  B )  =  ( B  u.  C
)
41, 2, 33eqtr4g 2310 1  |-  ( A  =  B  ->  ( C  u.  A )  =  ( C  u.  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    = wceq 1619    u. cun 3076
This theorem is referenced by:  uneq12  3234  uneq2i  3236  uneq2d  3239  uneqin  3327  disjssun  3419  uniprg  3742  sucprc  4360  unexb  4411  undifixp  6738  unxpdom  6955  ackbij1lem16  7745  fin23lem28  7850  ttukeylem6  8025  ipodrsima  14112  mplsubglem  16011  mretopd  16661  iscldtop  16664  dfcon2  16977  nconsubb  16981  spanun  21954  axfelem9  23522  brsuccf  23654  rankung  23970  domfldref  24226  repfuntw  24326  comppfsc  25473  nacsfix  25953  eldioph4b  26060  eldioph4i  26061  fiuneneq  26679  paddval  28676  dochsatshp  30330
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-v 2729  df-un 3083
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