Theorem orduniss 4570

Description: An ordinal class includes its union. (Contributed by NM, 13-Sep-2003.)

Assertion

Ref	Expression
orduniss	|- ( Ord A -> U. A C_ A )

Proof of Theorem orduniss

Step	Hyp	Ref	Expression
1		ordtr 4523	. 2 |- ( Ord A -> Tr A )
2		df-tr 4230	. 2 |- ( Tr A <-> U. A C_ A )
3	1, 2	sylib 122	1 |- ( Ord A -> U. A C_ A )

This proof depends on syntax axioms:   -> wi 4   C_ wss 3220   U.cuni 3935   Tr wtr 4229   Ord word 4507

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106

This proof depends on definitions:  df-bi 117  df-tr 4230  df-iord 4511

This theorem is used by:  ordunisuc2r  4661  limom  4761