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Theorem snm 3650
Description: The singleton of a set is inhabited. (Contributed by Jim Kingdon, 11-Aug-2018.)
Hypothesis
Ref Expression
snnz.1 𝐴 ∈ V
Assertion
Ref Expression
snm 𝑥 𝑥 ∈ {𝐴}
Distinct variable group:   𝑥,𝐴

Proof of Theorem snm
StepHypRef Expression
1 snnz.1 . 2 𝐴 ∈ V
2 snmg 3648 . 2 (𝐴 ∈ V → ∃𝑥 𝑥 ∈ {𝐴})
31, 2ax-mp 5 1 𝑥 𝑥 ∈ {𝐴}
Colors of variables: wff set class
Syntax hints:  wex 1469  wcel 1481  Vcvv 2689  {csn 3531
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-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-sn 3537
This theorem is referenced by:  mss  4155  ssfilem  6776  diffitest  6788  djuexb  6936  exmidonfinlem  7065  exmidfodomrlemim  7073  cc2lem  7097
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