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Definition df-ord 4868
Description: Define the ordinal predicate, which is true for a class that is transitive and is well-ordered by the epsilon relation. Variant of definition of [BellMachover] p. 468. (Contributed by NM, 17-Sep-1993.)
Assertion
Ref Expression
df-ord  |-  ( Ord 
A  <->  ( Tr  A  /\  _E  We  A ) )

Detailed syntax breakdown of Definition df-ord
StepHypRef Expression
1 cA . . 3  class  A
21word 4864 . 2  wff  Ord  A
31wtr 4527 . . 3  wff  Tr  A
4 cep 4776 . . . 4  class  _E
51, 4wwe 4824 . . 3  wff  _E  We  A
63, 5wa 369 . 2  wff  ( Tr  A  /\  _E  We  A )
72, 6wb 184 1  wff  ( Ord 
A  <->  ( Tr  A  /\  _E  We  A ) )
Colors of variables: wff setvar class
This definition is referenced by:  ordeq  4872  ordwe  4878  ordtr  4879  trssord  4882  ordelord  4887  ord0  4917  ordon  6600  dford2  8037  smobeth  8961  gruina  9196  dford5reg  29186  dfon2  29196
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