ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfriota1 Unicode version

Theorem nfriota1 5863
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 5855 . 2  |-  ( iota_ x  e.  A  ph )  =  ( iota x
( x  e.  A  /\  ph ) )
2 nfiota1 5201 . 2  |-  F/_ x
( iota x ( x  e.  A  /\  ph ) )
31, 2nfcxfr 2329 1  |-  F/_ x
( iota_ x  e.  A  ph )
Colors of variables: wff set class
Syntax hints:    /\ wa 104    e. wcel 2160   F/_wnfc 2319   iotacio 5197   iota_crio 5854
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-rex 2474  df-sn 3616  df-uni 3828  df-iota 5199  df-riota 5855
This theorem is referenced by:  riotaprop  5879  riotass2  5882  riotass  5883  lble  8939  oddpwdclemdvds  12213  oddpwdclemndvds  12214
  Copyright terms: Public domain W3C validator