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Theorem unisuc 4959
Description: A transitive class is equal to the union of its successor. Combines Theorem 4E of [Enderton] p. 72 and Exercise 6 of [Enderton] p. 73. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
unisuc.1
Assertion
Ref Expression
unisuc

Proof of Theorem unisuc
StepHypRef Expression
1 ssequn1 3673 . 2
2 df-tr 4546 . 2
3 df-suc 4889 . . . . 5
43unieqi 4258 . . . 4
5 uniun 4268 . . . 4
6 unisuc.1 . . . . . 6
76unisn 4264 . . . . 5
87uneq2i 3654 . . . 4
94, 5, 83eqtri 2490 . . 3
109eqeq1i 2464 . 2
111, 2, 103bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  =wceq 1395  e.wcel 1818   cvv 3109  u.cun 3473  C_wss 3475  {csn 4029  U.cuni 4249  Trwtr 4545  succsuc 4885
This theorem is referenced by:  onunisuci  4996  ordunisuc  6667
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-v 3111  df-un 3480  df-in 3482  df-ss 3489  df-sn 4030  df-pr 4032  df-uni 4250  df-tr 4546  df-suc 4889
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