Theorem dford3 4514

Description: Alias for df-iord 4513. Use it instead of df-iord 4513 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 4513	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 4231   Ord word 4509

This proof depends on definitions:  df-iord 4513

This theorem is used by:  ordeq  4519  ordtr  4525  trssord  4527  ordelord  4528  ord0  4538  ordon  4635  ordsucim  4649  onintonm  4666  ordom  4756  exmidonfinlem  7551  pw1on  7591  bj-nnord  17189  bj-omord  17191