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Theorem iuneq2i 3731
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 3729 . 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 2428 1  |-  U_ x  e.  A  B  =  U_ x  e.  A  C
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1287    e. wcel 1436   U_ciun 3713
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 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-ral 2360  df-rex 2361  df-v 2617  df-in 2994  df-ss 3001  df-iun 3715
This theorem is referenced by:  dfiunv2  3749  iunrab  3760  iunid  3768  iunin1  3777  2iunin  3779  resiun1  4699  resiun2  4700  dfimafn2  5317  dfmpt  5437  rdgival  6101  uniqs  6302
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