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Theorem iotanul 4354
 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 2208 . 2
2 dfiota2 4340 . . 3
3 alnex 1543 . . . . . 6
4 ax-1 5 . . . . . . . . . . 11
5 eqidd 2354 . . . . . . . . . . 11
64, 5impbid1 194 . . . . . . . . . 10
76con2bid 319 . . . . . . . . 9
87alimi 1559 . . . . . . . 8
9 abbi 2463 . . . . . . . 8
108, 9sylib 188 . . . . . . 7
11 dfnul2 3552 . . . . . . 7
1210, 11syl6eqr 2403 . . . . . 6
133, 12sylbir 204 . . . . 5
1413unieqd 3902 . . . 4
15 uni0 3918 . . . 4
1614, 15syl6eq 2401 . . 3
172, 16syl5eq 2397 . 2
181, 17sylnbi 297 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176  wal 1540  wex 1541   wceq 1642  weu 2204  cab 2339  c0 3550  cuni 3891  cio 4337 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-ral 2619  df-rex 2620  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-ss 3259  df-nul 3551  df-sn 3741  df-uni 3892  df-iota 4339 This theorem is referenced by:  iotassuni  4355  iotaex  4356  dfiota3  4370  dfiota4  4372  fvprc  5325
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