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Theorem uneq1d 3235
 Description: Deduction adding union to the right in a class equality. (Contributed by NM, 29-Mar-1998.)
Hypothesis
Ref Expression
uneq1d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
uneq1d (𝜑 → (𝐴𝐶) = (𝐵𝐶))

Proof of Theorem uneq1d
StepHypRef Expression
1 uneq1d.1 . 2 (𝜑𝐴 = 𝐵)
2 uneq1 3229 . 2 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
31, 2syl 14 1 (𝜑 → (𝐴𝐶) = (𝐵𝐶))
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1332   ∪ cun 3075 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2692  df-un 3081 This theorem is referenced by:  ifeq1  3483  preq1  3609  tpeq1  3618  tpeq2  3619  resasplitss  5311  fmptpr  5621  funresdfunsnss  5632  rdgisucinc  6291  oasuc  6369  omsuc  6377  funresdfunsndc  6411  fisseneq  6830  sbthlemi5  6859  exmidfodomrlemim  7077  fzpred  9901  fseq1p1m1  9925  nn0split  9964  nnsplit  9965  fzo0sn0fzo1  10049  fzosplitprm1  10062  fsum1p  11239  zsupcllemstep  11694  setsvala  12049  setsabsd  12057  setscom  12058
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