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Definition df-ord 5764
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 5760 . 2 wff Ord 𝐴
31wtr 4785 . . 3 wff Tr 𝐴
4 cep 5057 . . . 4 class E
51, 4wwe 5101 . . 3 wff E We 𝐴
63, 5wa 383 . 2 wff (Tr 𝐴 ∧ E We 𝐴)
72, 6wb 196 1 wff (Ord 𝐴 ↔ (Tr 𝐴 ∧ E We 𝐴))
Colors of variables: wff setvar class
This definition is referenced by:  ordeq  5768  ordwe  5774  ordtr  5775  trssord  5778  ordelord  5783  ord0  5815  ordon  7024  dfrecs3  7514  dford2  8555  smobeth  9446  gruina  9678  dford5  31734  dford5reg  31811  dfon2  31821
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