Theorem dford3 4369

Description: Alias for df-iord 4368. Use it instead of df-iord 4368 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 4368	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 104   ↔ wb 105  ∀wral 2455  Tr wtr 4103  Ord word 4364

This theorem depends on definitions:  df-iord 4368

This theorem is referenced by:  ordeq  4374  ordtr  4380  trssord  4382  ordelord  4383  ord0  4393  ordon  4487  ordsucim  4501  onintonm  4518  ordom  4608  exmidonfinlem  7194  pw1on  7227  bj-nnord  14795  bj-omord  14797