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Theorem onunisuci 4392
 Description: An ordinal number is equal to the union of its successor. (Contributed by NM, 12-Jun-1994.)
Hypothesis
Ref Expression
on.1
Assertion
Ref Expression
onunisuci

Proof of Theorem onunisuci
StepHypRef Expression
1 on.1 . . 3
21ontrci 4387 . 2
31elexi 2724 . . 3
43unisuc 4373 . 2
52, 4mpbi 144 1
 Colors of variables: wff set class Syntax hints:   wceq 1335   wcel 2128  cuni 3772   wtr 4062  con0 4323   csuc 4325 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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ral 2440  df-rex 2441  df-v 2714  df-un 3106  df-in 3108  df-ss 3115  df-sn 3566  df-pr 3567  df-uni 3773  df-tr 4063  df-iord 4326  df-on 4328  df-suc 4331 This theorem is referenced by: (None)
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