Theorem dford3 4512

Description: Alias for df-iord 4511. Use it instead of df-iord 4511 for naming consistency with set.mm. (Contributed by Jim Kingdon, 10-Oct-2018.)

Assertion

Ref	Expression
dford3	|- ( Ord A <-> ( Tr A /\ A. x e. A Tr x ) )

Distinct variable group:   x, A

Proof of Theorem dford3

Step	Hyp	Ref	Expression
1		df-iord 4511	1 |- ( Ord A <-> ( Tr A /\ A. x e. A Tr x ) )

This proof depends on syntax axioms:   /\ wa 104   <-> wb 105   A.wral 2528   Tr wtr 4229   Ord word 4507

This proof depends on definitions:  df-iord 4511

This theorem is used by:  ordeq  4517  ordtr  4523  trssord  4525  ordelord  4526  ord0  4536  ordon  4633  ordsucim  4647  onintonm  4664  ordom  4754  exmidonfinlem  7545  pw1on  7585  bj-nnord  16984  bj-omord  16986