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Theorem nfriota1 6239
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 6232 . 2  |-  ( iota_ x  e.  A  ph )  =  ( iota x
( x  e.  A  /\  ph ) )
2 nfiota1 5536 . 2  |-  F/_ x
( iota x ( x  e.  A  /\  ph ) )
31, 2nfcxfr 2614 1  |-  F/_ x
( iota_ x  e.  A  ph )
Colors of variables: wff setvar class
Syntax hints:    /\ wa 367    e. wcel 1823   F/_wnfc 2602   iotacio 5532   iota_crio 6231
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ral 2809  df-rex 2810  df-sn 4017  df-uni 4236  df-iota 5534  df-riota 6232
This theorem is referenced by:  riotaprop  6255  riotass2  6258  riotass  6259  riotaxfrd  6262  lble  10490  riotaneg  10513  zriotaneg  10974  riotaocN  35350  ltrniotaval  36723  cdlemksv2  36989  cdlemkuv2  37009  cdlemk36  37055
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