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Theorem onunisuci 4354
 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 4349 . 2 Tr 𝐴
31elexi 2698 . . 3 𝐴 ∈ V
43unisuc 4335 . 2 (Tr 𝐴 suc 𝐴 = 𝐴)
52, 4mpbi 144 1 suc 𝐴 = 𝐴
 Colors of variables: wff set class Syntax hints:   = wceq 1331   ∈ wcel 1480  ∪ cuni 3736  Tr wtr 4026  Oncon0 4285  suc csuc 4287 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-sn 3533  df-pr 3534  df-uni 3737  df-tr 4027  df-iord 4288  df-on 4290  df-suc 4293 This theorem is referenced by: (None)
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