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Theorem nfiota1 5361
Description: Bound-variable hypothesis builder for the  iota class. (Contributed by Andrew Salmon, 11-Jul-2011.) (Revised by Mario Carneiro, 15-Oct-2016.)
Assertion
Ref Expression
nfiota1  |-  F/_ x
( iota x ph )

Proof of Theorem nfiota1
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 dfiota2 5360 . 2  |-  ( iota
x ph )  =  U. { y  |  A. x ( ph  <->  x  =  y ) }
2 nfaba1 2529 . . 3  |-  F/_ x { y  |  A. x ( ph  <->  x  =  y ) }
32nfuni 3964 . 2  |-  F/_ x U. { y  |  A. x ( ph  <->  x  =  y ) }
41, 3nfcxfr 2521 1  |-  F/_ x
( iota x ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 177   A.wal 1546   {cab 2374   F/_wnfc 2511   U.cuni 3958   iotacio 5357
This theorem is referenced by:  iota2df  5383  sniota  5386  opabiota  6475  nfriota1  6494  nfriotad  6495  erovlem  6937  bnj1366  28540
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2369
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2375  df-cleq 2381  df-clel 2384  df-nfc 2513  df-ral 2655  df-rex 2656  df-sn 3764  df-uni 3959  df-iota 5359
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