Theorem orduniss 4355

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 4308	. 2 |- ( Ord A -> Tr A )
2		df-tr 4035	. 2 |- ( Tr A <-> U. A C_ A )
3	1, 2	sylib 121	1 |- ( Ord A -> U. A C_ A )

Syntax hints:   -> wi 4   C_ wss 3076   U.cuni 3744   Tr wtr 4034   Ord word 4292

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105

This theorem depends on definitions:  df-bi 116  df-tr 4035  df-iord 4296

This theorem is referenced by:  ordunisuc2r  4438  limom  4535