Theorem dford3 4462

Description: Alias for df-iord 4461. Use it instead of df-iord 4461 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 4461	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 104   ↔ wb 105  ∀wral 2508  Tr wtr 4185  Ord word 4457

This theorem depends on definitions:  df-iord 4461

This theorem is referenced by:  ordeq  4467  ordtr  4473  trssord  4475  ordelord  4476  ord0  4486  ordon  4582  ordsucim  4596  onintonm  4613  ordom  4703  exmidonfinlem  7394  pw1on  7434  bj-nnord  16489  bj-omord  16491