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Theorem snelpwrOLD 28359
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 4323. Unlike snelpw 4323, 
A may be a proper class. The proof of this theorem was automatically generated from snelpwrVD 28358 using a tools command file, translateMWO.cmd , by translating the proof into its non-virtual deduction form and minimizing it. (Moved to snelpwi 4322 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 4322 1  |-  ( A  e.  B  ->  { A }  e.  ~P B
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1715   ~Pcpw 3714   {csn 3729
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-9 1659  ax-8 1680  ax-14 1719  ax-6 1734  ax-7 1739  ax-11 1751  ax-12 1937  ax-ext 2347  ax-sep 4243  ax-nul 4251  ax-pr 4316
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1324  df-ex 1547  df-nf 1550  df-sb 1654  df-clab 2353  df-cleq 2359  df-clel 2362  df-nfc 2491  df-ne 2531  df-v 2875  df-dif 3241  df-un 3243  df-in 3245  df-ss 3252  df-nul 3544  df-pw 3716  df-sn 3735  df-pr 3736
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