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Theorem iuneq2i 3923
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 3921 . 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 2612 1  |-  U_ x  e.  A  B  =  U_ x  e.  A  C
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623    e. wcel 1684   U_ciun 3905
This theorem is referenced by:  iunrab  3949  iunid  3957  iunin1  3967  2iunin  3970  resiundiOLD  4745  resiun1  4974  resiun2  4975  dfimafn2  5572  dfmpt  5701  funiunfv  5774  fpar  6222  onovuni  6359  abianfplem  6470  uniqs  6719  marypha2lem2  7189  alephlim  7694  cfsmolem  7896  ituniiun  8048  imasdsval2  13419  lpival  15997  cmpsublem  17126  txbasval  17301  uniioombllem2  18938  uniioombllem4  18941  volsup2  18960  itg1addlem5  19055  itg1climres  19069  sigaclfu2  23482  measvuni  23542  trpred0  24239  dfiunv2  25916  dfaimafn2  28028
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-v 2790  df-in 3159  df-ss 3166  df-iun 3907
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