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Definition df-ord 4613
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 4609 . 2  wff  Ord  A
31wtr 4327 . . 3  wff  Tr  A
4 cep 4521 . . . 4  class  _E
51, 4wwe 4569 . . 3  wff  _E  We  A
63, 5wa 360 . 2  wff  ( Tr  A  /\  _E  We  A )
72, 6wb 178 1  wff  ( Ord 
A  <->  ( Tr  A  /\  _E  We  A ) )
Colors of variables: wff set class
This definition is referenced by:  ordeq  4617  ordwe  4623  ordtr  4624  trssord  4627  ordelord  4632  ord0  4662  ordon  4792  dford2  7604  smobeth  8492  gruina  8724  dford5reg  25440  dfon2  25450
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