Theorem dford3 4488

Description: Alias for df-iord 4487. Use it instead of df-iord 4487 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 4487	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 104   ↔ wb 105  ∀wral 2520  Tr wtr 4208  Ord word 4483

This theorem depends on definitions:  df-iord 4487

This theorem is referenced by:  ordeq  4493  ordtr  4499  trssord  4501  ordelord  4502  ord0  4512  ordon  4608  ordsucim  4622  onintonm  4639  ordom  4729  exmidonfinlem  7496  pw1on  7536  bj-nnord  16728  bj-omord  16730