Theorem orduniss 6419

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 6334	. 2 ⊢ (Ord 𝐴 → Tr 𝐴)
2		df-tr 5210	. 2 ⊢ (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)
3	1, 2	sylib 218	1 ⊢ (Ord 𝐴 → ∪ 𝐴 ⊆ 𝐴)

Syntax hints:   → wi 4   ⊆ wss 3911  ∪ cuni 4867  Tr wtr 5209  Ord word 6319

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 207  df-an 396  df-tr 5210  df-ord 6323

This theorem is referenced by:  orduniorsuc  7785  onfununi  8287  rankuniss  9795  r1limwun  10665  ontgval  36392  onsupneqmaxlim0  43186  onsupnmax  43190