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Theorem onunisuci 6506
Description: An ordinal number is equal to the union of its successor. (Contributed by NM, 12-Jun-1994.)
Hypothesis
Ref Expression
on.1 𝐴 ∈ On
Assertion
Ref Expression
onunisuci suc 𝐴 = 𝐴

Proof of Theorem onunisuci
StepHypRef Expression
1 on.1 . 2 𝐴 ∈ On
2 onunisuc 6496 . 2 (𝐴 ∈ On → suc 𝐴 = 𝐴)
31, 2ax-mp 5 1 suc 𝐴 = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1537  wcel 2106   cuni 4912  Oncon0 6386  suc csuc 6388
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-ral 3060  df-v 3480  df-un 3968  df-ss 3980  df-sn 4632  df-pr 4634  df-uni 4913  df-tr 5266  df-po 5597  df-so 5598  df-fr 5641  df-we 5643  df-ord 6389  df-on 6390  df-suc 6392
This theorem is referenced by:  rankuni  9901  onsucconni  36420  onsucsuccmpi  36426  finxp1o  37375
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