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Theorem onunisuci 4223
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 . . 3 𝐴 ∈ On
21ontrci 4218 . 2 Tr 𝐴
31elexi 2622 . . 3 𝐴 ∈ V
43unisuc 4204 . 2 (Tr 𝐴 suc 𝐴 = 𝐴)
52, 4mpbi 143 1 suc 𝐴 = 𝐴
Colors of variables: wff set class
Syntax hints:   = wceq 1285  wcel 1434   cuni 3627  Tr wtr 3901  Oncon0 4154  suc csuc 4156
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-rex 2359  df-v 2614  df-un 2988  df-in 2990  df-ss 2997  df-sn 3428  df-pr 3429  df-uni 3628  df-tr 3902  df-iord 4157  df-on 4159  df-suc 4162
This theorem is referenced by: (None)
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