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Theorem unieqi 3658
Description: Inference of equality of two class unions. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
unieqi.1  |-  A  =  B
Assertion
Ref Expression
unieqi  |-  U. A  =  U. B

Proof of Theorem unieqi
StepHypRef Expression
1 unieqi.1 . 2  |-  A  =  B
2 unieq 3657 . 2  |-  ( A  =  B  ->  U. A  =  U. B )
31, 2ax-mp 7 1  |-  U. A  =  U. B
Colors of variables: wff set class
Syntax hints:    = 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:  elunirab  3661  unisn  3664  uniop  4073  unisuc  4231  unisucg  4232  univ  4288  dfiun3g  4678  op1sta  4899  op2nda  4902  dfdm2  4952  iotajust  4966  dfiota2  4968  cbviota  4972  sb8iota  4974  dffv4g  5286  funfvdm2f  5353  riotauni  5596  1st0  5897  2nd0  5898  unielxp  5926  brtpos0  5999  recsfval  6062  uniqs  6330  xpassen  6526  sup00  6677
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