Theorem dford3 4289

Description: Alias for df-iord 4288. Use it instead of df-iord 4288 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 4288	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 103   ↔ wb 104  ∀wral 2416  Tr wtr 4026  Ord word 4284

This theorem depends on definitions:  df-iord 4288

This theorem is referenced by:  ordeq  4294  ordtr  4300  trssord  4302  ordelord  4303  ord0  4313  ordon  4402  ordsucim  4416  onintonm  4433  ordom  4520  exmidonfinlem  7049  bj-nnord  13156  bj-omord  13158