Theorem dford3 4104

Description: Alias for df-iord 4103. Use it instead of df-iord 4103 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 4103	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 97   ↔ wb 98  ∀wral 2306  Tr wtr 3854  Ord word 4099

This theorem depends on definitions:  df-iord 4103

This theorem is referenced by:  ordeq  4109  ordtr  4115  trssord  4117  ordelord  4118  ord0  4128  ordon  4212  ordsucim  4226  onintonm  4243  ordom  4329  bj-nnord  10083  bj-omord  10085