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Theorem nfriota1 6312
Description: The abstraction variable in a restricted iota descriptor isn't free. (Contributed by NM, 12-Oct-2011.) (Revised by Mario Carneiro, 15-Oct-2016.)
Assertion
Ref Expression
nfriota1  |-  F/_ x
( iota_ x  e.  A ph )
Distinct variable group:    x, A
Allowed substitution hint:    ph( x)

Proof of Theorem nfriota1
StepHypRef Expression
1 df-riota 6304 . 2  |-  ( iota_ x  e.  A ph )  =  if ( E! x  e.  A  ph ,  ( iota x ( x  e.  A  /\  ph ) ) ,  (
Undef `  { x  |  x  e.  A }
) )
2 nfreu1 2710 . . 3  |-  F/ x E! x  e.  A  ph
3 nfiota1 5221 . . 3  |-  F/_ x
( iota x ( x  e.  A  /\  ph ) )
4 nfcv 2419 . . . 4  |-  F/_ x Undef
5 nfab1 2421 . . . 4  |-  F/_ x { x  |  x  e.  A }
64, 5nffv 5532 . . 3  |-  F/_ x
( Undef `  { x  |  x  e.  A } )
72, 3, 6nfif 3589 . 2  |-  F/_ x if ( E! x  e.  A  ph ,  ( iota x ( x  e.  A  /\  ph ) ) ,  (
Undef `  { x  |  x  e.  A }
) )
81, 7nfcxfr 2416 1  |-  F/_ x
( iota_ x  e.  A ph )
Colors of variables: wff set class
Syntax hints:    /\ wa 358    e. wcel 1684   {cab 2269   F/_wnfc 2406   E!wreu 2545   ifcif 3565   iotacio 5217   ` cfv 5255   Undefcund 6296   iota_crio 6297
This theorem is referenced by:  riotaprop  6328  riotass2  6332  riotass  6333  riotaxfrd  6336  riotasvdOLD  6348  lble  9706  riotaneg  9729  lineval22  26082  riotaocN  29399  ltrniotaval  30770  cdlemksv2  31036  cdlemkuv2  31056  cdlemk36  31102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-reu 2550  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-iota 5219  df-fv 5263  df-riota 6304
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