Theorem dford3 4399

Description: Alias for df-iord 4398. Use it instead of df-iord 4398 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 4398	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 104   ↔ wb 105  ∀wral 2472  Tr wtr 4128  Ord word 4394

This theorem depends on definitions:  df-iord 4398

This theorem is referenced by:  ordeq  4404  ordtr  4410  trssord  4412  ordelord  4413  ord0  4423  ordon  4519  ordsucim  4533  onintonm  4550  ordom  4640  exmidonfinlem  7255  pw1on  7288  bj-nnord  15520  bj-omord  15522