Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  trel3 Unicode version

Theorem trel3 4029
 Description: In a transitive class, the membership relation is transitive. (Contributed by NM, 19-Apr-1994.)
Assertion
Ref Expression
trel3

Proof of Theorem trel3
StepHypRef Expression
1 3anass 966 . . 3
2 trel 4028 . . . 4
32anim2d 335 . . 3
41, 3syl5bi 151 . 2
5 trel 4028 . 2
64, 5syld 45 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   w3a 962   wcel 1480   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-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-in 3072  df-ss 3079  df-uni 3732  df-tr 4022 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator