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Theorem sniota 4837
Description: A class abstraction with a unique member can be expressed as a singleton. (Contributed by Mario Carneiro, 23-Dec-2016.)
Assertion
Ref Expression
sniota  {  |  }  { iota }

Proof of Theorem sniota
StepHypRef Expression
1 nfeu1 1908 . . 3  F/
2 iota1 4824 . . . . 5  iota
3 eqcom 2039 . . . . 5 
iota 
iota
42, 3syl6bb 185 . . . 4  iota
5 abid 2025 . . . 4  {  |  }
6 vex 2554 . . . . 5 
_V
76elsnc 3390 . . . 4  { iota }  iota
84, 5, 73bitr4g 212 . . 3  {  |  } 
{ iota }
91, 8alrimi 1412 . 2  {  |  } 
{ iota }
10 nfab1 2177 . . 3  F/_ {  |  }
11 nfiota1 4812 . . . 4  F/_ iota
1211nfsn 3421 . . 3  F/_ { iota }
1310, 12cleqf 2198 . 2  {  |  }  { iota }  {  |  } 
{ iota }
149, 13sylibr 137 1  {  |  }  { iota }
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wal 1240   wceq 1242   wcel 1390  weu 1897   {cab 2023   {csn 3367   iotacio 4808
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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-sbc 2759  df-un 2916  df-sn 3373  df-pr 3374  df-uni 3572  df-iota 4810
This theorem is referenced by:  snriota  5440
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