Theorem dford3 4457

Description: Alias for df-iord 4456. Use it instead of df-iord 4456 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 4456	1 ⊢ (Ord 𝐴 ↔ (Tr 𝐴 ∧ ∀𝑥 ∈ 𝐴 Tr 𝑥))

Syntax hints:   ∧ wa 104   ↔ wb 105  ∀wral 2508  Tr wtr 4181  Ord word 4452

This theorem depends on definitions:  df-iord 4456

This theorem is referenced by:  ordeq  4462  ordtr  4468  trssord  4470  ordelord  4471  ord0  4481  ordon  4577  ordsucim  4591  onintonm  4608  ordom  4698  exmidonfinlem  7367  pw1on  7407  bj-nnord  16279  bj-omord  16281