MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-ord Structured version   Visualization version   Unicode version

Definition df-ord 5449
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 5445 . 2  wff  Ord  A
31wtr 4513 . . 3  wff  Tr  A
4 cep 4765 . . . 4  class  _E
51, 4wwe 4814 . . 3  wff  _E  We  A
63, 5wa 375 . 2  wff  ( Tr  A  /\  _E  We  A )
72, 6wb 189 1  wff  ( Ord 
A  <->  ( Tr  A  /\  _E  We  A ) )
Colors of variables: wff setvar class
This definition is referenced by:  ordeq  5453  ordwe  5459  ordtr  5460  trssord  5463  ordelord  5468  ord0  5498  ordon  6641  dfrecs3  7122  dford2  8156  smobeth  9042  gruina  9274  dford5reg  30478  dfon2  30488
  Copyright terms: Public domain W3C validator