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Theorem iuneq2i 3939
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 3937 . 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 2625 1  |-  U_ x  e.  A  B  =  U_ x  e.  A  C
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1632    e. wcel 1696   U_ciun 3921
This theorem is referenced by:  iunrab  3965  iunid  3973  iunin1  3983  2iunin  3986  resiundiOLD  4761  resiun1  4990  resiun2  4991  dfimafn2  5588  dfmpt  5717  funiunfv  5790  fpar  6238  onovuni  6375  abianfplem  6486  uniqs  6735  marypha2lem2  7205  alephlim  7710  cfsmolem  7912  ituniiun  8064  imasdsval2  13435  lpival  16013  cmpsublem  17142  txbasval  17317  uniioombllem2  18954  uniioombllem4  18957  volsup2  18976  itg1addlem5  19071  itg1climres  19085  sigaclfu2  23497  measvuni  23557  trpred0  24310  rabiun2  24997  dfiunv2  26019  dfaimafn2  28134
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-v 2803  df-in 3172  df-ss 3179  df-iun 3923
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