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Theorem unieqd 3659
Description: Deduction of equality of two class unions. (Contributed by NM, 21-Apr-1995.)
Hypothesis
Ref Expression
unieqd.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
unieqd  |-  ( ph  ->  U. A  =  U. B )

Proof of Theorem unieqd
StepHypRef Expression
1 unieqd.1 . 2  |-  ( ph  ->  A  =  B )
2 unieq 3657 . 2  |-  ( A  =  B  ->  U. A  =  U. B )
31, 2syl 14 1  |-  ( ph  ->  U. A  =  U. B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1289   U.cuni 3648
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rex 2365  df-uni 3649
This theorem is referenced by:  uniprg  3663  unisng  3665  unisn3  4261  onsucuni2  4370  opswapg  4904  elxp4  4905  elxp5  4906  iotaeq  4975  iotabi  4976  uniabio  4977  funfvdm  5351  funfvdm2  5352  fvun1  5354  fniunfv  5523  funiunfvdm  5524  1stvalg  5895  2ndvalg  5896  fo1st  5910  fo2nd  5911  f1stres  5912  f2ndres  5913  2nd1st  5932  cnvf1olem  5971  brtpos2  5998  dftpos4  6010  tpostpos  6011  recseq  6053  tfrexlem  6081  xpcomco  6522  xpassen  6526  xpdom2  6527  supeq1  6660  supeq2  6663  supeq3  6664  supeq123d  6665  en2other2  6801  dfinfre  8389  hashinfom  10151  hashennn  10153  fsumcnv  10794  peano4nninf  11542
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