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

Theorem snm 3518
 Description: The singleton of a set is inhabited. (Contributed by Jim Kingdon, 11-Aug-2018.)
Hypothesis
Ref Expression
snnz.1
Assertion
Ref Expression
snm
Distinct variable group:   ,

Proof of Theorem snm
StepHypRef Expression
1 snnz.1 . 2
2 snmg 3516 . 2
31, 2ax-mp 7 1
 Colors of variables: wff set class Syntax hints:  wex 1422   wcel 1434  cvv 2602  csn 3406 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-sn 3412 This theorem is referenced by:  mss  3989  ssfilem  6410  diffitest  6421
 Copyright terms: Public domain W3C validator