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Theorem uneq1i 3134
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 3131 . 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 1285    u. cun 2982
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 2614  df-un 2988
This theorem is referenced by:  un12  3142  unundi  3145  tpcoma  3510  qdass  3513  qdassr  3514  tpidm12  3515  resasplitss  5138  fmptpr  5431  df2o3  6127  undifdc  6561  exmidfodomrlemim  6730  znnen  10991
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