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Theorem snmg 3477
 Description: The singleton of a set is inhabited. (Contributed by Jim Kingdon, 11-Aug-2018.)
Assertion
Ref Expression
snmg (A 𝑉x x {A})
Distinct variable group:   x,A
Allowed substitution hint:   𝑉(x)

Proof of Theorem snmg
StepHypRef Expression
1 snidg 3392 . 2 (A 𝑉A {A})
2 elex2 2564 . 2 (A {A} → x x {A})
31, 2syl 14 1 (A 𝑉x x {A})
 Colors of variables: wff set class Syntax hints:   → wi 4  ∃wex 1378   ∈ wcel 1390  {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-bndl 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-v 2553  df-sn 3373 This theorem is referenced by:  snm  3479  prmg  3480  xpimasn  4712  1stconst  5784  2ndconst  5785
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