Theorem dford3 4470

Description: Alias for df-iord 4469. Use it instead of df-iord 4469 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 4469	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 104   ↔ wb 105  ∀wral 2511  Tr wtr 4192  Ord word 4465

This theorem depends on definitions:  df-iord 4469

This theorem is referenced by:  ordeq  4475  ordtr  4481  trssord  4483  ordelord  4484  ord0  4494  ordon  4590  ordsucim  4604  onintonm  4621  ordom  4711  exmidonfinlem  7447  pw1on  7487  bj-nnord  16657  bj-omord  16659