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Theorem ordtr 4081
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 4070 . 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 2300  Tr wtr 3845  Ord word 4065
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 4069
This theorem is referenced by:  ordelss  4082  ordin  4088  ordtr1  4091  orduniss  4128  ontrci  4130  ordon  4178  ordsucim  4192  ordsucss  4196  onsucsssucr  4200  ordsucunielexmid  4216  nlimsucg  4242  ordpwsucss  4243  tfrexlem  5889
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