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Theorem snelpwrOLD 28607
Description: If a class is contained in another class, then its singleton is contained in the power class of that other class. This theorem is the left-to-right implication of the biconditional snelpw 4221. Unlike snelpw 4221, 
A may be a proper class. The proof of this theorem was automatically generated from snelpwrVD 28606 using a tools command file, translateMWO.cmd , by translating the proof into its non-virtual deduction form and minimizing it. (Moved to snelpwi 4220 in main set.mm and may be deleted by mathbox owner, AS. --NM 10-Sep-2013.) (Contributed by Alan Sare, 25-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
snelpwrOLD  |-  ( A  e.  B  ->  { A }  e.  ~P B
)

Proof of Theorem snelpwrOLD
StepHypRef Expression
1 snelpwi 4220 1  |-  ( A  e.  B  ->  { A }  e.  ~P B
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1684   ~Pcpw 3625   {csn 3640
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-pw 3627  df-sn 3646  df-pr 3647
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