Theorem orduniss 6266

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 6186	. 2 ⊢ (Ord 𝐴 → Tr 𝐴)
2		df-tr 5137	. 2 ⊢ (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)
3	1, 2	sylib 221	1 ⊢ (Ord 𝐴 → ∪ 𝐴 ⊆ 𝐴)

Syntax hints:   → wi 4   ⊆ wss 3843  ∪ cuni 4796  Tr wtr 5136  Ord word 6171

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 210  df-an 400  df-tr 5137  df-ord 6175

This theorem is referenced by:  orduniorsuc  7564  onfununi  8007  rankuniss  9368  r1limwun  10236  ontgval  34258