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

Theorem nfriota1 5705
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 𝑥(𝑥𝐴 𝜑)
Distinct variable group:   𝑥,𝐴
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem nfriota1
StepHypRef Expression
1 df-riota 5698 . 2 (𝑥𝐴 𝜑) = (℩𝑥(𝑥𝐴𝜑))
2 nfiota1 5060 . 2 𝑥(℩𝑥(𝑥𝐴𝜑))
31, 2nfcxfr 2255 1 𝑥(𝑥𝐴 𝜑)
Colors of variables: wff set class
Syntax hints:  wa 103  wcel 1465  wnfc 2245  cio 5056  crio 5697
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-rex 2399  df-sn 3503  df-uni 3707  df-iota 5058  df-riota 5698
This theorem is referenced by:  riotaprop  5721  riotass2  5724  riotass  5725  lble  8673  oddpwdclemdvds  11775  oddpwdclemndvds  11776
  Copyright terms: Public domain W3C validator