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Theorem selpw 3341
Description: Setvar variable membership in a power class (common case). See elpw 3340. (Contributed by David A. Wheeler, 8-Dec-2018.)
Assertion
Ref Expression
selpw (x 𝒫 AxA)
Distinct variable group:   x,A

Proof of Theorem selpw
StepHypRef Expression
1 vex 2538 . 2 x V
21elpw 3340 1 (x 𝒫 AxA)
Colors of variables: wff set class
Syntax hints:  wb 98   wcel 1374  wss 2894  𝒫 cpw 3334
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537  df-in 2901  df-ss 2908  df-pw 3336
This theorem is referenced by:  ordpwsucss  4227  fabexg  5002  abexssex  5675  qsss  6076  npsspw  6325
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