Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  sniota Unicode version

Theorem sniota 5125
 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

Proof of Theorem sniota
StepHypRef Expression
1 nfeu1 2011 . . 3
2 iota1 5112 . . . . 5
3 eqcom 2142 . . . . 5
42, 3syl6bb 195 . . . 4
5 abid 2128 . . . 4
6 vex 2693 . . . . 5
76elsn 3549 . . . 4
84, 5, 73bitr4g 222 . . 3
91, 8alrimi 1503 . 2
10 nfab1 2284 . . 3
11 nfiota1 5100 . . . 4
1211nfsn 3592 . . 3
1310, 12cleqf 2306 . 2
149, 13sylibr 133 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wal 1330   wceq 1332   wcel 1481  weu 2000  cab 2126  csn 3533  cio 5096 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-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-eu 2003  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423  df-v 2692  df-sbc 2915  df-un 3081  df-sn 3539  df-pr 3540  df-uni 3746  df-iota 5098 This theorem is referenced by:  snriota  5769
 Copyright terms: Public domain W3C validator