Theorem orduniss 6461

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 6378	. 2 ⊢ (Ord 𝐴 → Tr 𝐴)
2		df-tr 5266	. 2 ⊢ (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)
3	1, 2	sylib 217	1 ⊢ (Ord 𝐴 → ∪ 𝐴 ⊆ 𝐴)

Syntax hints:   → wi 4   ⊆ wss 3948  ∪ cuni 4908  Tr wtr 5265  Ord word 6363

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 397  df-tr 5266  df-ord 6367

This theorem is referenced by:  orduniorsuc  7820  onfununi  8343  rankuniss  9863  r1limwun  10733  ontgval  35619  onsupneqmaxlim0  42275  onsupnmax  42279