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Theorem snssi 3536
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 (𝐴𝐵 → {𝐴} ⊆ 𝐵)

Proof of Theorem snssi
StepHypRef Expression
1 snssg 3528 . 2 (𝐴𝐵 → (𝐴𝐵 ↔ {𝐴} ⊆ 𝐵))
21ibi 169 1 (𝐴𝐵 → {𝐴} ⊆ 𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1409  wss 2945  {csn 3403
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-in 2952  df-ss 2959  df-sn 3409
This theorem is referenced by:  difsnss  3538  sssnm  3553  tpssi  3558  snelpwi  3976  intid  3988  ordsucss  4258  xpsspw  4478  djussxp  4509  xpimasn  4797  fconst6g  5113  fvimacnvi  5309  fsn2  5365  fnressn  5377  fsnunf  5390  axresscn  6994  nn0ssre  8243  1fv  9098  1exp  9449
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