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Theorem orduniss 6283
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 6203 . 2 (Ord 𝐴 → Tr 𝐴)
2 df-tr 5170 . 2 (Tr 𝐴 𝐴𝐴)
31, 2sylib 219 1 (Ord 𝐴 𝐴𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3940   cuni 4837  Tr wtr 5169  Ord word 6188
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 208  df-an 397  df-tr 5170  df-ord 6192
This theorem is referenced by:  orduniorsuc  7533  onfununi  7969  rankuniss  9284  r1limwun  10147  ontgval  33663
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