Theorem dford3 4402

Description: Alias for df-iord 4401. Use it instead of df-iord 4401 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 4401	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 104   ↔ wb 105  ∀wral 2475  Tr wtr 4131  Ord word 4397

This theorem depends on definitions:  df-iord 4401

This theorem is referenced by:  ordeq  4407  ordtr  4413  trssord  4415  ordelord  4416  ord0  4426  ordon  4522  ordsucim  4536  onintonm  4553  ordom  4643  exmidonfinlem  7260  pw1on  7293  bj-nnord  15604  bj-omord  15606