Theorem orduniss 6413

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 6328	. 2 ⊢ (Ord 𝐴 → Tr 𝐴)
2		df-tr 5183	. 2 ⊢ (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)
3	1, 2	sylib 220	1 ⊢ (Ord 𝐴 → ∪ 𝐴 ⊆ 𝐴)

Syntax hints:   → wi 4   ⊆ wss 3885  ∪ cuni 4841  Tr wtr 5182  Ord word 6313

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 209  df-an 398  df-tr 5183  df-ord 6317

This theorem is referenced by:  orduniorsuc  7774  onfununi  8275  rankuniss  9785  r1limwun  10654  ontgval  36674  onsupneqmaxlim0  43684  onsupnmax  43688