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Theorem selpw 3366
Description: Setvar variable membership in a power class (common case). See elpw 3365. (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 2560 . 2 𝑥 ∈ V
21elpw 3365 1 (𝑥 ∈ 𝒫 𝐴𝑥𝐴)
Colors of variables: wff set class
Syntax hints:  wb 98  wcel 1393  wss 2917  𝒫 cpw 3359
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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-in 2924  df-ss 2931  df-pw 3361
This theorem is referenced by:  ordpwsucss  4291  fabexg  5077  abexssex  5752  qsss  6165  npsspw  6567
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