Theorem orduniss 4180

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 4133	. 2 |- ( Ord A -> Tr A )
2		df-tr 3876	. 2 |- ( Tr A <-> U. A C_ A )
3	1, 2	sylib 120	1 |- ( Ord A -> U. A C_ A )

Syntax hints:   -> wi 4   C_ wss 2973   U.cuni 3601   Tr wtr 3875   Ord word 4117

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104

This theorem depends on definitions:  df-bi 115  df-tr 3876  df-iord 4121

This theorem is referenced by:  ordunisuc2r  4258  limom  4354