ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfriota Structured version   GIF 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 xφ
nfriota.2 xA
Assertion
Ref Expression
nfriota x(y A φ)
Distinct variable group:   x,y
Allowed substitution hints:   φ(x,y)   A(x,y)

Proof of Theorem nfriota
StepHypRef Expression
1 nftru 1352 . . 3 y
2 nfriota.1 . . . 4 xφ
32a1i 9 . . 3 ( ⊤ → Ⅎxφ)
4 nfriota.2 . . . 4 xA
54a1i 9 . . 3 ( ⊤ → xA)
61, 3, 5nfriotadxy 5419 . 2 ( ⊤ → x(y A φ))
76trud 1251 1 x(y A φ)
Colors of variables: wff set class
Syntax hints:  wtru 1243  wnf 1346  wnfc 2162  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