Theorem orduniss 5738

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 5654	. 2 ⊢ (Ord 𝐴 → Tr 𝐴)
2		df-tr 4681	. 2 ⊢ (Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴)
3	1, 2	sylib 207	1 ⊢ (Ord 𝐴 → ∪ 𝐴 ⊆ 𝐴)

Syntax hints:   → wi 4   ⊆ wss 3540  ∪ cuni 4372  Tr wtr 4680  Ord word 5639

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 196  df-an 385  df-tr 4681  df-ord 5643

This theorem is referenced by:  orduniorsuc  6922  onfununi  7325  rankuniss  8612  r1limwun  9437  ontgval  31600