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Theorem pwidg 3364
Description: Membership of the original in a power set. (Contributed by Stefan O'Rear, 1-Feb-2015.)
Assertion
Ref Expression
pwidg  V  ~P

Proof of Theorem pwidg
StepHypRef Expression
1 ssid 2958 . 2  C_
2 elpwg 3359 . 2  V  ~P  C_
31, 2mpbiri 157 1  V  ~P
Colors of variables: wff set class
Syntax hints:   wi 4   wcel 1390    C_ wss 2911   ~Pcpw 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-bndl 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:  pwid  3365  axpweq  3915
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