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

Theorem setind 4454
 Description: Set (epsilon) induction. Theorem 5.22 of [TakeutiZaring] p. 21. (Contributed by NM, 17-Sep-2003.)
Assertion
Ref Expression
setind
Distinct variable group:   ,

Proof of Theorem setind
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfss2 3086 . . . 4
21imbi1i 237 . . 3
32albii 1446 . 2
4 setindel 4453 . 2
53, 4sylbi 120 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1329   wceq 1331   wcel 1480  cvv 2686   wss 3071 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-setind 4452 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-ral 2421  df-v 2688  df-in 3077  df-ss 3084 This theorem is referenced by:  setind2  4455
 Copyright terms: Public domain W3C validator