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Theorem iotanul 6158
 Description: Theorem 8.22 in [Quine] p. 57. This theorem is the result if there isn't exactly one that satisfies . (Contributed by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
iotanul

Proof of Theorem iotanul
StepHypRef Expression
1 df-eu 2118 . 2
2 dfiota2 6144 . . 3
3 alnex 1569 . . . . . 6
4 ax-1 7 . . . . . . . . . . 11
5 eqidd 2254 . . . . . . . . . . 11
64, 5impbid1 196 . . . . . . . . . 10
76con2bid 321 . . . . . . . . 9
87alimi 1546 . . . . . . . 8
9 abbi 2359 . . . . . . . 8
108, 9sylib 190 . . . . . . 7
11 dfnul2 3364 . . . . . . 7
1210, 11syl6eqr 2303 . . . . . 6
133, 12sylbir 206 . . . . 5
1413unieqd 3738 . . . 4
15 uni0 3752 . . . 4
1614, 15syl6eq 2301 . . 3
172, 16syl5eq 2297 . 2
181, 17sylnbi 299 1
 Colors of variables: wff set class Syntax hints:   wn 5   wi 6   wb 178  wal 1532  wex 1537   wceq 1619  weu 2114  cab 2239  c0 3362  cuni 3727  cio 6141 This theorem is referenced by:  iotassuni  6159  iotaex  6160  riotav  6195  riotaprc  6228  isf32lem9  7871  grpidval  14219  0g0  14221 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-eu 2118  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-ral 2513  df-rex 2514  df-v 2729  df-dif 3081  df-in 3085  df-ss 3089  df-nul 3363  df-sn 3550  df-uni 3728  df-iota 6143
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