Theorem dford3 4512

Description: Alias for df-iord 4511. Use it instead of df-iord 4511 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 4511	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

This proof depends on syntax axioms:   ∧ wa 104   ↔ wb 105  ∀wral 2528  Tr wtr 4229  Ord word 4507

This proof depends on definitions:  df-iord 4511

This theorem is used by:  ordeq  4517  ordtr  4523  trssord  4525  ordelord  4526  ord0  4536  ordon  4633  ordsucim  4647  onintonm  4664  ordom  4754  exmidonfinlem  7545  pw1on  7585  bj-nnord  16984  bj-omord  16986