MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  orduniss Structured version   Visualization version   GIF version

Theorem orduniss 6266
Description: An ordinal class includes its union. (Contributed by NM, 13-Sep-2003.)
Assertion
Ref Expression
orduniss (Ord 𝐴 𝐴𝐴)

Proof of Theorem orduniss
StepHypRef Expression
1 ordtr 6186 . 2 (Ord 𝐴 → Tr 𝐴)
2 df-tr 5137 . 2 (Tr 𝐴 𝐴𝐴)
31, 2sylib 221 1 (Ord 𝐴 𝐴𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3843   cuni 4796  Tr wtr 5136  Ord word 6171
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 210  df-an 400  df-tr 5137  df-ord 6175
This theorem is referenced by:  orduniorsuc  7564  onfununi  8007  rankuniss  9368  r1limwun  10236  ontgval  34258
  Copyright terms: Public domain W3C validator