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

Theorem nfriota 5420
Description: A variable not free in a wff remains so in a restricted iota descriptor. (Contributed by NM, 12-Oct-2011.)
Hypotheses
Ref Expression
nfriota.1  F/
nfriota.2  F/_
Assertion
Ref Expression
nfriota  F/_ iota_
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem nfriota
StepHypRef Expression
1 nftru 1352 . . 3  F/
2 nfriota.1 . . . 4  F/
32a1i 9 . . 3  F/
4 nfriota.2 . . . 4  F/_
54a1i 9 . . 3  F/_
61, 3, 5nfriotadxy 5419 . 2  F/_ iota_
76trud 1251 1  F/_ iota_
Colors of variables: wff set class
Syntax hints:   wtru 1243   F/wnf 1346   F/_wnfc 2162   iota_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:  csbriotag  5423
  Copyright terms: Public domain W3C validator