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Theorem uneq1i 3196
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 (𝐴𝐶) = (𝐵𝐶)

Proof of Theorem uneq1i
StepHypRef Expression
1 uneq1i.1 . 2 𝐴 = 𝐵
2 uneq1 3193 . 2 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
31, 2ax-mp 5 1 (𝐴𝐶) = (𝐵𝐶)
Colors of variables: wff set class
Syntax hints:   = wceq 1316  cun 3039
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-un 3045
This theorem is referenced by:  un12  3204  unundi  3207  tpcoma  3587  qdass  3590  qdassr  3591  tpidm12  3592  resasplitss  5272  fmptpr  5580  df2o3  6295  undifdc  6780  sbthlemi6  6818  exmidfodomrlemim  7025  znnen  11838  setscom  11926
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