Theorem orduni 4488

Description: The union of an ordinal class is ordinal. (Contributed by NM, 12-Sep-2003.)

Assertion

Ref	Expression
orduni	|- ( Ord A -> Ord U. A )

Proof of Theorem orduni

Step	Hyp	Ref	Expression
1		ordsson 4485	. 2 |- ( Ord A -> A C_ On )
2		ssorduni 4480	. 2 |- ( A C_ On -> Ord U. A )
3	1, 2	syl 14	1 |- ( Ord A -> Ord U. A )

Syntax hints:   -> wi 4   C_ wss 3127   U.cuni 3805   Ord word 4356   Oncon0 4357

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1445  ax-7 1446  ax-gen 1447  ax-ie1 1491  ax-ie2 1492  ax-8 1502  ax-10 1503  ax-11 1504  ax-i12 1505  ax-bndl 1507  ax-4 1508  ax-17 1524  ax-i9 1528  ax-ial 1532  ax-i5r 1533  ax-ext 2157

This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1459  df-sb 1761  df-clab 2162  df-cleq 2168  df-clel 2171  df-nfc 2306  df-ral 2458  df-rex 2459  df-v 2737  df-in 3133  df-ss 3140  df-uni 3806  df-tr 4097  df-iord 4360  df-on 4362

This theorem is referenced by:  tfrcl  6355