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Theorem nfriota1 5813
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 5806 . 2  |-  ( iota_ x  e.  A  ph )  =  ( iota x
( x  e.  A  /\  ph ) )
2 nfiota1 5160 . 2  |-  F/_ x
( iota x ( x  e.  A  /\  ph ) )
31, 2nfcxfr 2309 1  |-  F/_ x
( iota_ x  e.  A  ph )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    e. wcel 2141   F/_wnfc 2299   iotacio 5156   iota_crio 5805
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-rex 2454  df-sn 3587  df-uni 3795  df-iota 5158  df-riota 5806
This theorem is referenced by:  riotaprop  5829  riotass2  5832  riotass  5833  lble  8850  oddpwdclemdvds  12111  oddpwdclemndvds  12112
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