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Theorem iotanul 5568
 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
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-eu 2323 . 2
2 dfiota2 5554 . . 3
3 alnex 1673 . . . . . 6
4 ax-1 6 . . . . . . . . . . 11
5 eqidd 2472 . . . . . . . . . . 11
64, 5impbid1 208 . . . . . . . . . 10
76con2bid 336 . . . . . . . . 9
87alimi 1692 . . . . . . . 8
9 abbi 2585 . . . . . . . 8
108, 9sylib 201 . . . . . . 7
11 dfnul2 3724 . . . . . . 7
1210, 11syl6eqr 2523 . . . . . 6
133, 12sylbir 218 . . . . 5
1413unieqd 4200 . . . 4
15 uni0 4217 . . . 4
1614, 15syl6eq 2521 . . 3
172, 16syl5eq 2517 . 2
181, 17sylnbi 313 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 189  wal 1450   wceq 1452  wex 1671  weu 2319  cab 2457  c0 3722  cuni 4190  cio 5551 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-v 3033  df-dif 3393  df-in 3397  df-ss 3404  df-nul 3723  df-sn 3960  df-uni 4191  df-iota 5553 This theorem is referenced by:  iotassuni  5569  iotaex  5570  dfiota4  5581  csbiota  5582  tz6.12-2  5870  dffv3  5875  csbriota  6282  riotaund  6305  isf32lem9  8809  grpidval  16581  0g0  16584
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