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Theorem snsspw 3962
 Description: The singleton of a class is a subset of its power class. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
snsspw

Proof of Theorem snsspw
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqimss 3392 . . 3
2 elsn 3821 . . 3
3 df-pw 3793 . . . 4
43abeq2i 2542 . . 3
51, 2, 43imtr4i 258 . 2
65ssriv 3344 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   wcel 1725   wss 3312  cpw 3791  csn 3806 This theorem is referenced by:  snexALT  4377  snwf  7725  tsksn  8625 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-in 3319  df-ss 3326  df-pw 3793  df-sn 3812
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