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Definition df-ord 5628
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 5624 . 2 wff Ord 𝐴
31wtr 4674 . . 3 wff Tr 𝐴
4 cep 4936 . . . 4 class E
51, 4wwe 4985 . . 3 wff E We 𝐴
63, 5wa 382 . 2 wff (Tr 𝐴 ∧ E We 𝐴)
72, 6wb 194 1 wff (Ord 𝐴 ↔ (Tr 𝐴 ∧ E We 𝐴))
Colors of variables: wff setvar class
This definition is referenced by:  ordeq  5632  ordwe  5638  ordtr  5639  trssord  5642  ordelord  5647  ord0  5679  ordon  6851  dfrecs3  7333  dford2  8377  smobeth  9264  gruina  9496  dford5reg  30724  dfon2  30734
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