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Theorem unisuc 4484
 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 3358 . 2
2 df-tr 4130 . 2
3 df-suc 4414 . . . . 5
43unieqi 3853 . . . 4
5 uniun 3862 . . . 4
6 unisuc.1 . . . . . 6
76unisn 3859 . . . . 5
87uneq2i 3339 . . . 4
94, 5, 83eqtri 2320 . . 3
109eqeq1i 2303 . 2
111, 2, 103bitr4i 268 1
 Colors of variables: wff set class Syntax hints:   wb 176   wceq 1632   wcel 1696  cvv 2801   cun 3163   wss 3165  csn 3653  cuni 3843   wtr 4129   csuc 4410 This theorem is referenced by:  onunisuci  4522  ordunisuc  4639 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562  df-v 2803  df-un 3170  df-in 3172  df-ss 3179  df-sn 3659  df-pr 3660  df-uni 3844  df-tr 4130  df-suc 4414
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