Theorem dford3 4507

Description: Alias for df-iord 4506. Use it instead of df-iord 4506 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 4506	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 104   ↔ wb 105  ∀wral 2528  Tr wtr 4224  Ord word 4502

This theorem depends on definitions:  df-iord 4506

This theorem is referenced by:  ordeq  4512  ordtr  4518  trssord  4520  ordelord  4521  ord0  4531  ordon  4628  ordsucim  4642  onintonm  4659  ordom  4749  exmidonfinlem  7535  pw1on  7575  bj-nnord  16898  bj-omord  16900