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Theorem nfiu1 3949
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 3923 . 2  |-  U_ x  e.  A  B  =  { y  |  E. x  e.  A  y  e.  B }
2 nfre1 2612 . . 3  |-  F/ x E. x  e.  A  y  e.  B
32nfab 2436 . 2  |-  F/_ x { y  |  E. x  e.  A  y  e.  B }
41, 3nfcxfr 2429 1  |-  F/_ x U_ x  e.  A  B
Colors of variables: wff set class
Syntax hints:    e. wcel 1696   {cab 2282   F/_wnfc 2419   E.wrex 2557   U_ciun 3921
This theorem is referenced by:  ssiun2s  3962  disjxiun  4036  triun  4142  eliunxp  4839  opeliunxp2  4840  ixpf  6854  ixpiunwdom  7321  r1val1  7474  rankuni2b  7541  rankval4  7555  cplem2  7576  ac6num  8122  iunfo  8177  iundom2g  8178  inar1  8413  tskuni  8421  gsum2d2lem  15240  gsum2d2  15241  gsumcom2  15242  iuncon  17170  ptclsg  17325  ssiun2sf  23173  bnj958  29288  bnj1000  29289  bnj981  29298  bnj1398  29380  bnj1408  29382
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562  df-iun 3923
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