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

Definition df-ord 6162
Description: Define the ordinal predicate, which is true for a class that is transitive and is well-ordered by the membership 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 6158 . 2 wff Ord 𝐴
31wtr 5136 . . 3 wff Tr 𝐴
4 cep 5429 . . . 4 class E
51, 4wwe 5477 . . 3 wff E We 𝐴
63, 5wa 399 . 2 wff (Tr 𝐴 ∧ E We 𝐴)
72, 6wb 209 1 wff (Ord 𝐴 ↔ (Tr 𝐴 ∧ E We 𝐴))
Colors of variables: wff setvar class
This definition is referenced by:  ordeq  6166  ordwe  6172  ordtr  6173  trssord  6176  ordelord  6181  ord0  6211  ordon  7478  dfrecs3  7992  dford2  9067  smobeth  9997  gruina  10229  dford5  33070  dford5reg  33140  dfon2  33150
  Copyright terms: Public domain W3C validator