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Theorem uneq2i 3197
Description: Inference adding union to the left in a class equality. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
uneq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
uneq2i (𝐶𝐴) = (𝐶𝐵)

Proof of Theorem uneq2i
StepHypRef Expression
1 uneq1i.1 . 2 𝐴 = 𝐵
2 uneq2 3194 . 2 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))
31, 2ax-mp 5 1 (𝐶𝐴) = (𝐶𝐵)
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:  un4  3206  unundir  3208  difun2  3412  difdifdirss  3417  qdass  3590  qdassr  3591  unisuc  4305  iunsuc  4312  fmptap  5578  fvsnun1  5585  rdgival  6247  rdg0  6252  undifdc  6780  exmidfodomrlemim  7025  djuassen  7041  facnn  10441  fac0  10442  fsum2dlemstep  11171  fsumiun  11214
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