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

Theorem riotacl 5406
Description: Closure of restricted iota. (Contributed by NM, 21-Aug-2011.)
Assertion
Ref Expression
riotacl  iota_
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem riotacl
StepHypRef Expression
1 ssrab2 3002 . 2  {  |  }  C_
2 riotacl2 5405 . 2  iota_  {  |  }
31, 2sseldi 2920 1  iota_
Colors of variables: wff set class
Syntax hints:   wi 4   wcel 1374  wreu 2286   {crab 2288   iota_crio 5392
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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-eu 1885  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-rex 2290  df-reu 2291  df-rab 2293  df-v 2537  df-sbc 2742  df-un 2899  df-in 2901  df-ss 2908  df-sn 3356  df-pr 3357  df-uni 3555  df-iota 4794  df-riota 5393
This theorem is referenced by:  riotaprop  5415  riotass2  5418  riotass  5419  acexmidlemcase  5431  subval  6796  subcl  6803
  Copyright terms: Public domain W3C validator