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Theorem uneq2 3130
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 3129 . 2  |-  ( A  =  B  ->  ( A  u.  C )  =  ( B  u.  C ) )
2 uncom 3126 . 2  |-  ( C  u.  A )  =  ( A  u.  C
)
3 uncom 3126 . 2  |-  ( C  u.  B )  =  ( B  u.  C
)
41, 2, 33eqtr4g 2140 1  |-  ( A  =  B  ->  ( C  u.  A )  =  ( C  u.  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1285    u. cun 2980
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-un 2986
This theorem is referenced by:  uneq12  3131  uneq2i  3133  uneq2d  3136  uneqin  3231  disjssun  3323  uniprg  3636  sucprc  4195  unexb  4223  unfiexmid  6462  unfidisj  6466  hashunlem  9880  bdunexb  10978  bj-unexg  10979
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