Theorem onuniss2 4523

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 3855	1 |- ( A e. On -> U. { x e. On | x C_ A } = A )

Syntax hints:   -> wi 4   = wceq 1363   e. wcel 2158   {crab 2469   C_ wss 3141   U.cuni 3821   Oncon0 4375

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 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-ral 2470  df-rab 2474  df-v 2751  df-in 3147  df-ss 3154  df-uni 3822

This theorem is referenced by: (None)