Theorem dford3 4413

Description: Alias for df-iord 4412. Use it instead of df-iord 4412 for naming consistency with set.mm. (Contributed by Jim Kingdon, 10-Oct-2018.)

Assertion

Ref	Expression
dford3	⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Distinct variable group:   𝑥,𝐴

Proof of Theorem dford3

Step	Hyp	Ref	Expression
1		df-iord 4412	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 104   ↔ wb 105  ∀wral 2483  Tr wtr 4141  Ord word 4408

This theorem depends on definitions:  df-iord 4412

This theorem is referenced by:  ordeq  4418  ordtr  4424  trssord  4426  ordelord  4427  ord0  4437  ordon  4533  ordsucim  4547  onintonm  4564  ordom  4654  exmidonfinlem  7300  pw1on  7337  bj-nnord  15856  bj-omord  15858