Theorem dford3 4352

Description: Alias for df-iord 4351. Use it instead of df-iord 4351 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 4351	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 103   ↔ wb 104  ∀wral 2448  Tr wtr 4087  Ord word 4347

This theorem depends on definitions:  df-iord 4351

This theorem is referenced by:  ordeq  4357  ordtr  4363  trssord  4365  ordelord  4366  ord0  4376  ordon  4470  ordsucim  4484  onintonm  4501  ordom  4591  exmidonfinlem  7170  pw1on  7203  bj-nnord  13993  bj-omord  13995