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Definition df-ord 5381
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 5377 . 2  wff  Ord  A
31wtr 4454 . . 3  wff  Tr  A
4 cep 4698 . . . 4  class  _E
51, 4wwe 4747 . . 3  wff  _E  We  A
63, 5wa 370 . 2  wff  ( Tr  A  /\  _E  We  A )
72, 6wb 187 1  wff  ( Ord 
A  <->  ( Tr  A  /\  _E  We  A ) )
Colors of variables: wff setvar class
This definition is referenced by:  ordeq  5385  ordwe  5391  ordtr  5392  trssord  5395  ordelord  5400  ord0  5430  ordon  6560  dfrecs3  7039  dford2  8071  smobeth  8955  gruina  9187  dford5reg  30372  dfon2  30382
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