Theorem dford3 4493

Description: Alias for df-iord 4492. Use it instead of df-iord 4492 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 4492	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 104   ↔ wb 105  ∀wral 2522  Tr wtr 4213  Ord word 4488

This theorem depends on definitions:  df-iord 4492

This theorem is referenced by:  ordeq  4498  ordtr  4504  trssord  4506  ordelord  4507  ord0  4517  ordon  4613  ordsucim  4627  onintonm  4644  ordom  4734  exmidonfinlem  7509  pw1on  7549  bj-nnord  16854  bj-omord  16856