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Theorem uneq1i 3150
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 3147 . 2  |-  ( A  =  B  ->  ( A  u.  C )  =  ( B  u.  C ) )
31, 2ax-mp 7 1  |-  ( A  u.  C )  =  ( B  u.  C
)
Colors of variables: wff set class
Syntax hints:    = wceq 1289    u. cun 2997
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-un 3003
This theorem is referenced by:  un12  3158  unundi  3161  tpcoma  3534  qdass  3537  qdassr  3538  tpidm12  3539  resasplitss  5184  fmptpr  5483  df2o3  6187  undifdc  6624  sbthlemi6  6661  exmidfodomrlemim  6817  znnen  11476
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