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Definition df-ord 6188
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 6184 . 2 wff Ord 𝐴
31wtr 5164 . . 3 wff Tr 𝐴
4 cep 5458 . . . 4 class E
51, 4wwe 5507 . . 3 wff E We 𝐴
63, 5wa 396 . 2 wff (Tr 𝐴 ∧ E We 𝐴)
72, 6wb 207 1 wff (Ord 𝐴 ↔ (Tr 𝐴 ∧ E We 𝐴))
Colors of variables: wff setvar class
This definition is referenced by:  ordeq  6192  ordwe  6198  ordtr  6199  trssord  6202  ordelord  6207  ord0  6237  ordon  7486  dfrecs3  8000  dford2  9072  smobeth  9997  gruina  10229  dford5  32855  dford5reg  32925  dfon2  32935
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