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

Theorem ordtr 4064
Description: An ordinal class is transitive. (Contributed by NM, 3-Apr-1994.)
Assertion
Ref Expression
ordtr (Ord A → Tr A)

Proof of Theorem ordtr
Dummy variable x is distinct from all other variables.
StepHypRef Expression
1 dford3 4053 . 2 (Ord A ↔ (Tr A x A Tr x))
21simplbi 259 1 (Ord A → Tr A)
Colors of variables: wff set class
Syntax hints:  wi 4  wral 2284  Tr wtr 3828  Ord word 4048
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99
This theorem depends on definitions:  df-bi 110  df-iord 4052
This theorem is referenced by:  ordelss  4065  ordin  4071  ordtr1  4074  orduniss  4112  ontrci  4114  ordon  4162  ordsucim  4176  ordsucss  4180  onsucsssucr  4184  ordsucunielexmid  4200  nlimsucg  4226  ordpwsucss  4227  tfrexlem  5870
  Copyright terms: Public domain W3C validator