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Theorem eqsnm 3517
Description: Two ways to express that an inhabited set equals a singleton. (Contributed by Jim Kingdon, 11-Aug-2018.)
Assertion
Ref Expression
eqsnm  { }
Distinct variable groups:   ,   ,

Proof of Theorem eqsnm
StepHypRef Expression
1 dfss3 2929 . . 3 
C_  { }  { }
2 elsn 3382 . . . 4  { }
32ralbii 2324 . . 3  { }
41, 3bitri 173 . 2 
C_  { }
5 sssnm 3516 . 2  C_  { }  { }
64, 5syl5rbbr 184 1  { }
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98   wceq 1242  wex 1378   wcel 1390  wral 2300    C_ wss 2911   {csn 3367
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-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-v 2553  df-in 2918  df-ss 2925  df-sn 3373
This theorem is referenced by: (None)
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