Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  dftr3 Unicode version

Theorem dftr3 4025
 Description: An alternate way of defining a transitive class. Definition 7.1 of [TakeutiZaring] p. 35. (Contributed by NM, 29-Aug-1993.)
Assertion
Ref Expression
dftr3
Distinct variable group:   ,

Proof of Theorem dftr3
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dftr5 4024 . 2
2 dfss3 3082 . . 3
32ralbii 2439 . 2
41, 3bitr4i 186 1
 Colors of variables: wff set class Syntax hints:   wb 104   wcel 1480  wral 2414   wss 3066   wtr 4021 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 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ral 2419  df-v 2683  df-in 3072  df-ss 3079  df-uni 3732  df-tr 4022 This theorem is referenced by:  trss  4030  trin  4031  triun  4034  trint  4036  tron  4299  ssorduni  4398  bj-nntrans2  13139  bj-omtrans2  13144
 Copyright terms: Public domain W3C validator