Theorem dford3 4427

Description: Alias for df-iord 4426. Use it instead of df-iord 4426 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 4426	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 104   ↔ wb 105  ∀wral 2485  Tr wtr 4153  Ord word 4422

This theorem depends on definitions:  df-iord 4426

This theorem is referenced by:  ordeq  4432  ordtr  4438  trssord  4440  ordelord  4441  ord0  4451  ordon  4547  ordsucim  4561  onintonm  4578  ordom  4668  exmidonfinlem  7327  pw1on  7367  bj-nnord  16063  bj-omord  16065