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Definition df-ord 4584
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 4580 . 2  wff  Ord  A
31wtr 4302 . . 3  wff  Tr  A
4 cep 4492 . . . 4  class  _E
51, 4wwe 4540 . . 3  wff  _E  We  A
63, 5wa 359 . 2  wff  ( Tr  A  /\  _E  We  A )
72, 6wb 177 1  wff  ( Ord 
A  <->  ( Tr  A  /\  _E  We  A ) )
Colors of variables: wff set class
This definition is referenced by:  ordeq  4588  ordwe  4594  ordtr  4595  trssord  4598  ordelord  4603  ord0  4633  ordon  4763  dford2  7575  smobeth  8461  gruina  8693  dford5reg  25409  dfon2  25419
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