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Theorem uneq1i 3309
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 3306 . 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 1364    u. cun 3151
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-un 3157
This theorem is referenced by:  un12  3317  unundi  3320  tpcoma  3712  qdass  3715  qdassr  3716  tpidm12  3717  resasplitss  5433  fmptpr  5750  df2o3  6483  undifdc  6980  sbthlemi6  7021  exmidfodomrlemim  7261  znnen  12555  setscom  12658
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