Theorem dford3 4464

Description: Alias for df-iord 4463. Use it instead of df-iord 4463 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 4463	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 104   ↔ wb 105  ∀wral 2510  Tr wtr 4187  Ord word 4459

This theorem depends on definitions:  df-iord 4463

This theorem is referenced by:  ordeq  4469  ordtr  4475  trssord  4477  ordelord  4478  ord0  4488  ordon  4584  ordsucim  4598  onintonm  4615  ordom  4705  exmidonfinlem  7403  pw1on  7443  bj-nnord  16553  bj-omord  16555