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Definition df-ord 5436
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 5432 . 2  wff  Ord  A
31wtr 4511 . . 3  wff  Tr  A
4 cep 4754 . . . 4  class  _E
51, 4wwe 4803 . . 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  5440  ordwe  5446  ordtr  5447  trssord  5450  ordelord  5455  ord0  5485  ordon  6614  dfrecs3  7090  dford2  8116  smobeth  9000  gruina  9232  dford5reg  30212  dfon2  30222
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