Theorem dford3 4366

Description: Alias for df-iord 4365. Use it instead of df-iord 4365 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 4365	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 104   ↔ wb 105  ∀wral 2455  Tr wtr 4100  Ord word 4361

This theorem depends on definitions:  df-iord 4365

This theorem is referenced by:  ordeq  4371  ordtr  4377  trssord  4379  ordelord  4380  ord0  4390  ordon  4484  ordsucim  4498  onintonm  4515  ordom  4605  exmidonfinlem  7188  pw1on  7221  bj-nnord  14561  bj-omord  14563