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Theorem pwsnss 3740
 Description: The power set of a singleton. (Contributed by Jim Kingdon, 12-Aug-2018.)
Assertion
Ref Expression
pwsnss

Proof of Theorem pwsnss
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sssnr 3690 . . 3
21ss2abi 3176 . 2
3 dfpr2 3553 . 2
4 df-pw 3519 . 2
52, 3, 43sstr4i 3145 1
 Colors of variables: wff set class Syntax hints:   wo 698   wceq 1332  cab 2127   wss 3078  c0 3370  cpw 3517  csn 3534  cpr 3535 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-in1 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2123 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1732  df-clab 2128  df-cleq 2134  df-clel 2137  df-nfc 2272  df-v 2693  df-dif 3080  df-un 3082  df-in 3084  df-ss 3091  df-nul 3371  df-pw 3519  df-sn 3540  df-pr 3541 This theorem is referenced by:  pwpw0ss  3741
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