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Theorem unisuc 4361
 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 3255 . 2
2 df-tr 4011 . 2
3 df-suc 4291 . . . . 5
43unieqi 3737 . . . 4
5 uniun 3746 . . . 4
6 unisuc.1 . . . . . 6
76unisn 3743 . . . . 5
87uneq2i 3236 . . . 4
94, 5, 83eqtri 2277 . . 3
109eqeq1i 2260 . 2
111, 2, 103bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wb 178   wceq 1619   wcel 1621  cvv 2727   cun 3076   wss 3078  csn 3544  cuni 3727   wtr 4010   csuc 4287 This theorem is referenced by:  onunisuci  4397  ordunisuc  4514 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-rex 2514  df-v 2729  df-un 3083  df-in 3085  df-ss 3089  df-sn 3550  df-pr 3551  df-uni 3728  df-tr 4011  df-suc 4291
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