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Theorem uneq1i 3226
Description: Inference adding union to the right in a class equality. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
uneq1i.1  |-  A  =  B
Assertion
Ref Expression
uneq1i  |-  ( A  u.  C )  =  ( B  u.  C
)

Proof of Theorem uneq1i
StepHypRef Expression
1 uneq1i.1 . 2  |-  A  =  B
2 uneq1 3223 . 2  |-  ( A  =  B  ->  ( A  u.  C )  =  ( B  u.  C ) )
31, 2ax-mp 5 1  |-  ( A  u.  C )  =  ( B  u.  C
)
Colors of variables: wff set class
Syntax hints:    = wceq 1331    u. cun 3069
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075
This theorem is referenced by:  un12  3234  unundi  3237  tpcoma  3617  qdass  3620  qdassr  3621  tpidm12  3622  resasplitss  5302  fmptpr  5612  df2o3  6327  undifdc  6812  sbthlemi6  6850  exmidfodomrlemim  7062  znnen  11922  setscom  12013
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