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Theorem prelpwi 4699
Description: A pair of two sets belongs to the power class of a class containing those two sets. (Contributed by Thierry Arnoux, 10-Mar-2017.)
Assertion
Ref Expression
prelpwi

Proof of Theorem prelpwi
StepHypRef Expression
1 prssi 4186 . 2
2 prex 4694 . . 3
32elpw 4018 . 2
41, 3sylibr 212 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  e.wcel 1818  C_wss 3475  ~Pcpw 4012  {cpr 4031
This theorem is referenced by:  inelfi  7898  isdrs2  15568  usgra1  24373  usgraexmpl  24401  cusgraexi  24468  cusgrafilem2  24480  unelsiga  28134  measxun2  28181  lincvalpr  33019  ldepspr  33074  zlmodzxzldeplem3  33103  zlmodzxzldep  33105  ldepsnlinc  33109
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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
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-ne 2654  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-pw 4014  df-sn 4030  df-pr 4032
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