Theorem orduniss 5821

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 5737	. 2 ⊢ (Ord 𝐴 → Tr 𝐴)
2		df-tr 4753	. 2 ⊢ (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)
3	1, 2	sylib 208	1 ⊢ (Ord 𝐴 → ∪ 𝐴 ⊆ 𝐴)

Syntax hints:   → wi 4   ⊆ wss 3574  ∪ cuni 4436  Tr wtr 4752  Ord word 5722

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 197  df-an 386  df-tr 4753  df-ord 5726

This theorem is referenced by:  orduniorsuc  7030  onfununi  7438  rankuniss  8729  r1limwun  9558  ontgval  32430