Theorem orduniss 6461

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 6375	. 2 ⊢ (Ord 𝐴 → Tr 𝐴)
2		df-tr 5217	. 2 ⊢ (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)
3	1, 2	sylib 221	1 ⊢ (Ord 𝐴 → ∪ 𝐴 ⊆ 𝐴)

This proof depends on syntax axioms:   → wi 4   ⊆ wss 3902  ∪ cuni 4870  Tr wtr 5216  Ord word 6360

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-tr 5217  df-ord 6364

This theorem is used by:  orduniorsuc  7829  onfununi  8333  rankuniss  9851  r1limwun  10748  ontgval  37037  onsupneqmaxlim0  44052  onsupnmax  44056