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Theorem nfiu1 3716
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 3688 . 2  |-  U_ x  e.  A  B  =  { y  |  E. x  e.  A  y  e.  B }
2 nfre1 2408 . . 3  |-  F/ x E. x  e.  A  y  e.  B
32nfab 2224 . 2  |-  F/_ x { y  |  E. x  e.  A  y  e.  B }
41, 3nfcxfr 2217 1  |-  F/_ x U_ x  e.  A  B
Colors of variables: wff set class
Syntax hints:    e. wcel 1434   {cab 2068   F/_wnfc 2207   E.wrex 2350   U_ciun 3686
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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rex 2355  df-iun 3688
This theorem is referenced by:  ssiun2s  3730  triun  3896  eliunxp  4503  opeliunxp2  4504
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