Theorem dford3 4398

Description: Alias for df-iord 4397. Use it instead of df-iord 4397 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 4397	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 104   ↔ wb 105  ∀wral 2472  Tr wtr 4127  Ord word 4393

This theorem depends on definitions:  df-iord 4397

This theorem is referenced by:  ordeq  4403  ordtr  4409  trssord  4411  ordelord  4412  ord0  4422  ordon  4518  ordsucim  4532  onintonm  4549  ordom  4639  exmidonfinlem  7253  pw1on  7286  bj-nnord  15450  bj-omord  15452