Theorem onuniss2 4559

Description: The union of the ordinal subsets of an ordinal number is that number. (Contributed by Jim Kingdon, 2-Aug-2019.)

Assertion

Ref	Expression
onuniss2	|- ( A e. On -> U. { x e. On | x C_ A } = A )

Distinct variable group:   x, A

Proof of Theorem onuniss2

Step	Hyp	Ref	Expression
1		unimax 3883	1 |- ( A e. On -> U. { x e. On | x C_ A } = A )

Syntax hints:   -> wi 4   = wceq 1372   e. wcel 2175   {crab 2487   C_ wss 3165   U.cuni 3849   Oncon0 4409

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 710  ax-5 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557  ax-ext 2186

This theorem depends on definitions:  df-bi 117  df-tru 1375  df-nf 1483  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-nfc 2336  df-ral 2488  df-rab 2492  df-v 2773  df-in 3171  df-ss 3178  df-uni 3850

This theorem is referenced by: (None)