Theorem orduniss 2327

Description: An ordinal class includes its union.

Assertion

Ref	Expression
orduniss	⊢ (Ord A → ∪A ⊆ A)

Proof of Theorem orduniss

Step	Hyp	Ref	Expression
1		ordtr 2213	. 2 ⊢ (Ord A → Tr A)
2		df-tr 2042	. 2 ⊢ (Tr A ↔ ∪A ⊆ A)
3	1, 2	sylib 173	1 ⊢ (Ord A → ∪A ⊆ A)

Syntax hints:   → wi 2   ⊆ wss 1487  ∪cuni 1919  Tr wtr 2041  Ord word 2198

This theorem is referenced by:  orduniorsuc 2337

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198  df-tr 2042  df-ord 2202

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