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

Theorem orduniss 6360
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 6280 . 2 (Ord 𝐴 → Tr 𝐴)
2 df-tr 5192 . 2 (Tr 𝐴 𝐴𝐴)
31, 2sylib 217 1 (Ord 𝐴 𝐴𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3887   cuni 4839  Tr wtr 5191  Ord word 6265
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 206  df-an 397  df-tr 5192  df-ord 6269
This theorem is referenced by:  orduniorsuc  7677  onfununi  8172  rankuniss  9624  r1limwun  10492  ontgval  34620
  Copyright terms: Public domain W3C validator