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Theorem prsspwg 4187
Description: An unordered pair belongs to the power class of a class iff each member belongs to the class. (Contributed by Thierry Arnoux, 3-Oct-2016.) (Revised by NM, 18-Jan-2018.)
Assertion
Ref Expression
prsspwg

Proof of Theorem prsspwg
StepHypRef Expression
1 prssg 4185 . 2
2 elpwg 4020 . . 3
3 elpwg 4020 . . 3
42, 3bi2anan9 873 . 2
51, 4bitr3d 255 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  e.wcel 1818  C_wss 3475  ~Pcpw 4012  {cpr 4031
This theorem is referenced by:  prsspw  4202
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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