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Theorem iotanul 5115
 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 1993 . . 3
2 dfiota2 5101 . . . 4
3 alnex 1476 . . . . . . 7
4 ax-in2 605 . . . . . . . . . 10
54alimi 1432 . . . . . . . . 9
6 ss2ab 3172 . . . . . . . . 9
75, 6sylibr 133 . . . . . . . 8
8 dfnul2 3372 . . . . . . . 8
97, 8sseqtrrdi 3153 . . . . . . 7
103, 9sylbir 134 . . . . . 6
1110unissd 3770 . . . . 5
12 uni0 3773 . . . . 5
1311, 12sseqtrdi 3152 . . . 4
142, 13eqsstrid 3150 . . 3
151, 14sylnbi 668 . 2
16 ss0 3410 . 2
1715, 16syl 14 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 104  wal 1330   wceq 1332  wex 1469  weu 1990  cab 2127   wss 3078  c0 3370  cuni 3746  cio 5098 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2123 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-fal 1338  df-nf 1438  df-sb 1732  df-eu 1993  df-clab 2128  df-cleq 2134  df-clel 2137  df-nfc 2272  df-ral 2423  df-rex 2424  df-v 2693  df-dif 3080  df-in 3084  df-ss 3091  df-nul 3371  df-sn 3540  df-uni 3747  df-iota 5100 This theorem is referenced by:  tz6.12-2  5424  0fv  5468  riotaund  5776
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