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Theorem snm 3590
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 3588 . 2 (𝐴 ∈ V → ∃𝑥 𝑥 ∈ {𝐴})
31, 2ax-mp 7 1 𝑥 𝑥 ∈ {𝐴}
Colors of variables: wff set class
Syntax hints:  wex 1436  wcel 1448  Vcvv 2641  {csn 3474
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082
This theorem depends on definitions:  df-bi 116  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-v 2643  df-sn 3480
This theorem is referenced by:  mss  4086  ssfilem  6698  diffitest  6710  djuexb  6844  exmidfodomrlemim  6966
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