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Theorem rext 4116
 Description: A theorem similar to extensionality, requiring the existence of a singleton. Exercise 8 of [TakeutiZaring] p. 16. (Contributed by NM, 10-Aug-1993.)
Assertion
Ref Expression
rext
Distinct variable group:   ,,

Proof of Theorem rext
StepHypRef Expression
1 vex 2730 . . . 4
21snid 3571 . . 3
3 snex 4110 . . . 4
4 eleq2 2314 . . . . 5
5 eleq2 2314 . . . . 5
64, 5imbi12d 313 . . . 4
73, 6cla4v 2811 . . 3
82, 7mpi 18 . 2
9 elsn 3559 . . 3
10 equcomi 1822 . . 3
119, 10sylbi 189 . 2
128, 11syl 17 1
 Colors of variables: wff set class Syntax hints:   wi 6  wal 1532   wceq 1619   wcel 1621  csn 3544 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-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-sep 4038  ax-nul 4046  ax-pr 4108 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-ne 2414  df-v 2729  df-dif 3081  df-un 3083  df-nul 3363  df-sn 3550  df-pr 3551
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