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Theorem nfiu1 3843
Description: Bound-variable hypothesis builder for indexed union. (Contributed by NM, 12-Oct-2003.)
Assertion
Ref Expression
nfiu1  |-  F/_ x U_ x  e.  A  B

Proof of Theorem nfiu1
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 df-iun 3815 . 2  |-  U_ x  e.  A  B  =  { y  |  E. x  e.  A  y  e.  B }
2 nfre1 2476 . . 3  |-  F/ x E. x  e.  A  y  e.  B
32nfab 2286 . 2  |-  F/_ x { y  |  E. x  e.  A  y  e.  B }
41, 3nfcxfr 2278 1  |-  F/_ x U_ x  e.  A  B
Colors of variables: wff set class
Syntax hints:    e. wcel 1480   {cab 2125   F/_wnfc 2268   E.wrex 2417   U_ciun 3813
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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422  df-iun 3815
This theorem is referenced by:  ssiun2s  3857  triun  4039  eliunxp  4678  opeliunxp2  4679  opeliunxp2f  6135  ixpf  6614  ctiunctlemfo  11959
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