Theorem onuniss2 4496

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 3830	1 |- ( A e. On -> U. { x e. On | x C_ A } = A )

Syntax hints:   -> wi 4   = wceq 1348   e. wcel 2141   {crab 2452   C_ wss 3121   U.cuni 3796   Oncon0 4348

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-ral 2453  df-rab 2457  df-v 2732  df-in 3127  df-ss 3134  df-uni 3797

This theorem is referenced by: (None)