Theorem onuniss2 4548

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 3873	1 |- ( A e. On -> U. { x e. On | x C_ A } = A )

Syntax hints:   -> wi 4   = wceq 1364   e. wcel 2167   {crab 2479   C_ wss 3157   U.cuni 3839   Oncon0 4398

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-ral 2480  df-rab 2484  df-v 2765  df-in 3163  df-ss 3170  df-uni 3840

This theorem is referenced by: (None)