Theorem dford3 4514

Description: Alias for df-iord 4513. Use it instead of df-iord 4513 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 4513	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

This proof depends on syntax axioms:   ∧ wa 104   ↔ wb 105  ∀wral 2528  Tr wtr 4231  Ord word 4509

This proof depends on definitions:  df-iord 4513

This theorem is used by:  ordeq  4519  ordtr  4525  trssord  4527  ordelord  4528  ord0  4538  ordon  4635  ordsucim  4649  onintonm  4666  ordom  4756  exmidonfinlem  7551  pw1on  7591  bj-nnord  17189  bj-omord  17191