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Theorem nfriota1 6263
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 6256 . 2  |-  ( iota_ x  e.  A  ph )  =  ( iota x
( x  e.  A  /\  ph ) )
2 nfiota1 5559 . 2  |-  F/_ x
( iota x ( x  e.  A  /\  ph ) )
31, 2nfcxfr 2627 1  |-  F/_ x
( iota_ x  e.  A  ph )
Colors of variables: wff setvar class
Syntax hints:    /\ wa 369    e. wcel 1767   F/_wnfc 2615   iotacio 5555   iota_crio 6255
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2822  df-rex 2823  df-sn 4034  df-uni 4252  df-iota 5557  df-riota 6256
This theorem is referenced by:  riotaprop  6280  riotass2  6283  riotass  6284  riotaxfrd  6287  lble  10507  riotaneg  10530  zriotaneg  10986  riotaocN  34407  ltrniotaval  35778  cdlemksv2  36044  cdlemkuv2  36064  cdlemk36  36110
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