Theorem dford3 4122

Description: Alias for df-iord 4121. Use it instead of df-iord 4121 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 4121	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 102   ↔ wb 103  ∀wral 2348  Tr wtr 3875  Ord word 4117

This theorem depends on definitions:  df-iord 4121

This theorem is referenced by:  ordeq  4127  ordtr  4133  trssord  4135  ordelord  4136  ord0  4146  ordon  4230  ordsucim  4244  onintonm  4261  ordom  4347  bj-nnord  10753  bj-omord  10755