Theorem orduni 4593

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 4590	. 2 |- ( Ord A -> A C_ On )
2		ssorduni 4585	. 2 |- ( A C_ On -> Ord U. A )
3	1, 2	syl 14	1 |- ( Ord A -> Ord U. A )

Syntax hints:   -> wi 4   C_ wss 3200   U.cuni 3893   Ord word 4459   Oncon0 4460

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-3an 1006  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-ral 2515  df-rex 2516  df-v 2804  df-in 3206  df-ss 3213  df-uni 3894  df-tr 4188  df-iord 4463  df-on 4465

This theorem is referenced by:  tfrcl  6529