Theorem orduniss 6360

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 6280	. 2 ⊢ (Ord 𝐴 → Tr 𝐴)
2		df-tr 5192	. 2 ⊢ (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)
3	1, 2	sylib 217	1 ⊢ (Ord 𝐴 → ∪ 𝐴 ⊆ 𝐴)

Syntax hints:   → wi 4   ⊆ wss 3887  ∪ cuni 4839  Tr wtr 5191  Ord word 6265

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 5192  df-ord 6269

This theorem is referenced by:  orduniorsuc  7677  onfununi  8172  rankuniss  9624  r1limwun  10492  ontgval  34620