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 Description: An unordered pair belongs to the power class of a class iff each member belongs to the class. (Contributed by NM, 10-Dec-2003.) (Proof shortened by OpenAI, 25-Mar-2020.)
Hypotheses
Ref Expression
Assertion
Ref Expression

Proof of Theorem prsspw
StepHypRef Expression
1 prsspw.1 . 2
2 prsspw.2 . 2
3 prsspwg 4187 . 2
41, 2, 3mp2an 672 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  /\wa 369  e.wcel 1818   cvv 3109  C_wss 3475  ~Pcpw 4012  {cpr 4031 This theorem is referenced by:  altxpsspw  29627 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3480  df-in 3482  df-ss 3489  df-pw 4014  df-sn 4030  df-pr 4032
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