Theorem dford3 4458

Description: Alias for df-iord 4457. Use it instead of df-iord 4457 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 4457	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 104   ↔ wb 105  ∀wral 2508  Tr wtr 4182  Ord word 4453

This theorem depends on definitions:  df-iord 4457

This theorem is referenced by:  ordeq  4463  ordtr  4469  trssord  4471  ordelord  4472  ord0  4482  ordon  4578  ordsucim  4592  onintonm  4609  ordom  4699  exmidonfinlem  7382  pw1on  7422  bj-nnord  16376  bj-omord  16378