Theorem dford3 4130

Description: Alias for df-iord 4129. Use it instead of df-iord 4129 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 4129	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 102   ↔ wb 103  ∀wral 2349  Tr wtr 3883  Ord word 4125

This theorem depends on definitions:  df-iord 4129

This theorem is referenced by:  ordeq  4135  ordtr  4141  trssord  4143  ordelord  4144  ord0  4154  ordon  4238  ordsucim  4252  onintonm  4269  ordom  4355  bj-nnord  10938  bj-omord  10940