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Theorem snm 3613
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 3611 . 2 (𝐴 ∈ V → ∃𝑥 𝑥 ∈ {𝐴})
31, 2ax-mp 5 1 𝑥 𝑥 ∈ {𝐴}
Colors of variables: wff set class
Syntax hints:  wex 1453  wcel 1465  Vcvv 2660  {csn 3497
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-sn 3503
This theorem is referenced by:  mss  4118  ssfilem  6737  diffitest  6749  djuexb  6897  exmidonfinlem  7017  exmidfodomrlemim  7025
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