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Theorem unieqd 3747
Description: Deduction of equality of two class unions. (Contributed by NM, 21-Apr-1995.)
Hypothesis
Ref Expression
unieqd.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
unieqd (𝜑 𝐴 = 𝐵)

Proof of Theorem unieqd
StepHypRef Expression
1 unieqd.1 . 2 (𝜑𝐴 = 𝐵)
2 unieq 3745 . 2 (𝐴 = 𝐵 𝐴 = 𝐵)
31, 2syl 14 1 (𝜑 𝐴 = 𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1331   cuni 3736
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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422  df-uni 3737
This theorem is referenced by:  uniprg  3751  unisng  3753  unisn3  4366  onsucuni2  4479  opswapg  5025  elxp4  5026  elxp5  5027  iotaeq  5096  iotabi  5097  uniabio  5098  funfvdm  5484  funfvdm2  5485  fvun1  5487  fniunfv  5663  funiunfvdm  5664  1stvalg  6040  2ndvalg  6041  fo1st  6055  fo2nd  6056  f1stres  6057  f2ndres  6058  2nd1st  6078  cnvf1olem  6121  brtpos2  6148  dftpos4  6160  tpostpos  6161  recseq  6203  tfrexlem  6231  ixpsnf1o  6630  xpcomco  6720  xpassen  6724  xpdom2  6725  supeq1  6873  supeq2  6876  supeq3  6877  supeq123d  6878  en2other2  7052  dfinfre  8721  hashinfom  10531  hashennn  10533  fsumcnv  11213  isbasisg  12221  basis1  12224  baspartn  12227  tgval  12228  eltg  12231  ntrfval  12279  ntrval  12289  tgrest  12348  restuni2  12356  lmfval  12371  cnfval  12373  cnpfval  12374  txtopon  12441  txswaphmeolem  12499  peano4nninf  13230
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