Theorem orduniss 6460

Description: An ordinal class includes its union. (Contributed by NM, 13-Sep-2003.)

Assertion

Ref	Expression
orduniss	⊢ (Ord 𝐴 → ∪ 𝐴 ⊆ 𝐴)

Proof of Theorem orduniss

Step	Hyp	Ref	Expression
1		ordtr 6374	. 2 ⊢ (Ord 𝐴 → Tr 𝐴)
2		df-tr 5218	. 2 ⊢ (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)
3	1, 2	sylib 221	1 ⊢ (Ord 𝐴 → ∪ 𝐴 ⊆ 𝐴)

This proof depends on syntax axioms:   → wi 4   ⊆ wss 3904  ∪ cuni 4871  Tr wtr 5217  Ord word 6359

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 401  df-tr 5218  df-ord 6363

This theorem is used by:  orduniorsuc  7824  onfununi  8326  rankuniss  9836  r1limwun  10727  ontgval  36970  onsupneqmaxlim0  43979  onsupnmax  43983