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Theorem iuneq2i 3839
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 3837 . 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 2492 1  |-  U_ x  e.  A  B  =  U_ x  e.  A  C
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1332    e. wcel 1481   U_ciun 3821
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-v 2691  df-in 3082  df-ss 3089  df-iun 3823
This theorem is referenced by:  dfiunv2  3857  iunrab  3868  iunid  3876  iunin1  3885  2iunin  3887  resiun1  4846  resiun2  4847  dfimafn2  5479  dfmpt  5605  rdgival  6287  uniqs  6495  txbasval  12475
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