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Theorem iotanul 4882
 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 1903 . . 3
2 dfiota2 4868 . . . 4
3 alnex 1388 . . . . . . 7
4 ax-in2 545 . . . . . . . . . 10
54alimi 1344 . . . . . . . . 9
6 ss2ab 3008 . . . . . . . . 9
75, 6sylibr 137 . . . . . . . 8
8 dfnul2 3226 . . . . . . . 8
97, 8syl6sseqr 2992 . . . . . . 7
103, 9sylbir 125 . . . . . 6
1110unissd 3604 . . . . 5
12 uni0 3607 . . . . 5
1311, 12syl6sseq 2991 . . . 4
142, 13syl5eqss 2989 . . 3
151, 14sylnbi 603 . 2
16 ss0 3257 . 2
1715, 16syl 14 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 98  wal 1241   wceq 1243  wex 1381  weu 1900  cab 2026   wss 2917  c0 3224  cuni 3580  cio 4865 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-nf 1350  df-sb 1646  df-eu 1903  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-dif 2920  df-in 2924  df-ss 2931  df-nul 3225  df-sn 3381  df-uni 3581  df-iota 4867 This theorem is referenced by:  tz6.12-2  5169  0fv  5208  riotaund  5502
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