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Theorem selpw 3358
Description: Setvar variable membership in a power class (common case). See elpw 3357. (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 2554 . 2 x V
21elpw 3357 1 (x 𝒫 AxA)
Colors of variables: wff set class
Syntax hints:  wb 98   wcel 1390  wss 2911  𝒫 cpw 3351
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918  df-ss 2925  df-pw 3353
This theorem is referenced by:  ordpwsucss  4243  fabexg  5020  abexssex  5694  qsss  6101  npsspw  6453
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