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Theorem iuneq2i 4053
Description: Equality inference for indexed union. (Contributed by NM, 22-Oct-2003.)
Hypothesis
Ref Expression
iuneq2i.1  |-  ( x  e.  A  ->  B  =  C )
Assertion
Ref Expression
iuneq2i  |-  U_ x  e.  A  B  =  U_ x  e.  A  C

Proof of Theorem iuneq2i
StepHypRef Expression
1 iuneq2 4051 . 2  |-  ( A. x  e.  A  B  =  C  ->  U_ x  e.  A  B  =  U_ x  e.  A  C
)
2 iuneq2i.1 . 2  |-  ( x  e.  A  ->  B  =  C )
31, 2mprg 2718 1  |-  U_ x  e.  A  B  =  U_ x  e.  A  C
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649    e. wcel 1717   U_ciun 4035
This theorem is referenced by:  iunrab  4079  iunid  4087  iunin1  4097  2iunin  4100  resiun1  5105  resiun2  5106  dfimafn2  5715  dfmpt  5850  funiunfv  5934  fpar  6389  onovuni  6540  abianfplem  6651  uniqs  6900  marypha2lem2  7376  alephlim  7881  cfsmolem  8083  ituniiun  8235  imasdsval2  13669  lpival  16243  cmpsublem  17384  txbasval  17559  uniioombllem2  19342  uniioombllem4  19345  volsup2  19364  itg1addlem5  19459  itg1climres  19473  indval2  24208  sigaclfu2  24300  measvuni  24362  trpred0  25263  rabiun2  25949  voliunnfl  25955  dfaimafn2  27699
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-ral 2654  df-rex 2655  df-v 2901  df-in 3270  df-ss 3277  df-iun 4037
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