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Definition df-ord 5695
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 5691 . 2 wff Ord 𝐴
31wtr 4722 . . 3 wff Tr 𝐴
4 cep 4993 . . . 4 class E
51, 4wwe 5042 . . 3 wff E We 𝐴
63, 5wa 384 . 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  5699  ordwe  5705  ordtr  5706  trssord  5709  ordelord  5714  ord0  5746  ordon  6944  dfrecs3  7429  dford2  8477  smobeth  9368  gruina  9600  dford5  31370  dford5reg  31441  dfon2  31451
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