Theorem dford3 4403

Description: Alias for df-iord 4402. Use it instead of df-iord 4402 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 4402	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 104   ↔ wb 105  ∀wral 2475  Tr wtr 4132  Ord word 4398

This theorem depends on definitions:  df-iord 4402

This theorem is referenced by:  ordeq  4408  ordtr  4414  trssord  4416  ordelord  4417  ord0  4427  ordon  4523  ordsucim  4537  onintonm  4554  ordom  4644  exmidonfinlem  7272  pw1on  7309  bj-nnord  15688  bj-omord  15690