Theorem dford3 4414

Description: Alias for df-iord 4413. Use it instead of df-iord 4413 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 4413	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 104   ↔ wb 105  ∀wral 2484  Tr wtr 4142  Ord word 4409

This theorem depends on definitions:  df-iord 4413

This theorem is referenced by:  ordeq  4419  ordtr  4425  trssord  4427  ordelord  4428  ord0  4438  ordon  4534  ordsucim  4548  onintonm  4565  ordom  4655  exmidonfinlem  7301  pw1on  7338  bj-nnord  15894  bj-omord  15896