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

Theorem nfriota1 5418
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(x A φ)
Distinct variable group:   x,A
Allowed substitution hint:   φ(x)

Proof of Theorem nfriota1
StepHypRef Expression
1 df-riota 5411 . 2 (x A φ) = (℩x(x A φ))
2 nfiota1 4812 . 2 x(℩x(x A φ))
31, 2nfcxfr 2172 1 x(x A φ)
Colors of variables: wff set class
Syntax hints:   wa 97   wcel 1390  wnfc 2162  cio 4808  crio 5410
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-sn 3373  df-uni 3572  df-iota 4810  df-riota 5411
This theorem is referenced by:  riotaprop  5434  riotass2  5437  riotass  5438
  Copyright terms: Public domain W3C validator