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Theorem iotanul 5424
 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 2284 . 2
2 dfiota2 5410 . . 3
3 alnex 1552 . . . . . 6
4 ax-1 5 . . . . . . . . . . 11
5 eqidd 2436 . . . . . . . . . . 11
64, 5impbid1 195 . . . . . . . . . 10
76con2bid 320 . . . . . . . . 9
87alimi 1568 . . . . . . . 8
9 abbi 2545 . . . . . . . 8
108, 9sylib 189 . . . . . . 7
11 dfnul2 3622 . . . . . . 7
1210, 11syl6eqr 2485 . . . . . 6
133, 12sylbir 205 . . . . 5
1413unieqd 4018 . . . 4
15 uni0 4034 . . . 4
1614, 15syl6eq 2483 . . 3
172, 16syl5eq 2479 . 2
181, 17sylnbi 298 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177  wal 1549  wex 1550   wceq 1652  weu 2280  cab 2421  c0 3620  cuni 4007  cio 5407 This theorem is referenced by:  iotassuni  5425  iotaex  5426  dfiota4  5437  tz6.12-2  5710  dffv3  5715  riotav  6545  riotaprc  6578  isf32lem9  8230  grpidval  14695  0g0  14697 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-v 2950  df-dif 3315  df-in 3319  df-ss 3326  df-nul 3621  df-sn 3812  df-uni 4008  df-iota 5409
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