Theorem dford3 4345

Description: Alias for df-iord 4344. Use it instead of df-iord 4344 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 4344	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 103   ↔ wb 104  ∀wral 2444  Tr wtr 4080  Ord word 4340

This theorem depends on definitions:  df-iord 4344

This theorem is referenced by:  ordeq  4350  ordtr  4356  trssord  4358  ordelord  4359  ord0  4369  ordon  4463  ordsucim  4477  onintonm  4494  ordom  4584  exmidonfinlem  7149  pw1on  7182  bj-nnord  13840  bj-omord  13842