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Theorem snssi 3499
Description: The singleton of an element of a class is a subset of the class. (Contributed by NM, 6-Jun-1994.)
Assertion
Ref Expression
snssi (A B → {A} ⊆ B)

Proof of Theorem snssi
StepHypRef Expression
1 snssg 3491 . 2 (A B → (A B ↔ {A} ⊆ B))
21ibi 165 1 (A B → {A} ⊆ B)
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1390  wss 2911  {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-bnd 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-in 2918  df-ss 2925  df-sn 3373
This theorem is referenced by:  difsnss  3501  sssnm  3516  tpssi  3521  snelpwi  3939  intid  3951  ordsucss  4196  xpsspw  4393  djussxp  4424  xpimasn  4712  fconst6g  5028  fvimacnvi  5224  fsn2  5280  fnressn  5292  fsnunf  5305  axresscn  6706  nn0ssre  7921  1fv  8726  1exp  8898
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