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Theorem nfriota1 6059
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 6052 . 2  |-  ( iota_ x  e.  A  ph )  =  ( iota x
( x  e.  A  /\  ph ) )
2 nfiota1 5383 . 2  |-  F/_ x
( iota x ( x  e.  A  /\  ph ) )
31, 2nfcxfr 2576 1  |-  F/_ x
( iota_ x  e.  A  ph )
Colors of variables: wff setvar class
Syntax hints:    /\ wa 369    e. wcel 1756   F/_wnfc 2566   iotacio 5379   iota_crio 6051
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ral 2720  df-rex 2721  df-sn 3878  df-uni 4092  df-iota 5381  df-riota 6052
This theorem is referenced by:  riotaprop  6076  riotass2  6079  riotass  6080  riotaxfrd  6083  lble  10282  riotaneg  10305  zriotaneg  10754  riotaocN  32854  ltrniotaval  34225  cdlemksv2  34491  cdlemkuv2  34511  cdlemk36  34557
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