Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  pwel Unicode version

Theorem pwel 4148
 Description: Membership of a power class. Exercise 10 of [Enderton] p. 26. (Contributed by NM, 13-Jan-2007.)
Assertion
Ref Expression
pwel

Proof of Theorem pwel
StepHypRef Expression
1 elssuni 3772 . . 3
2 sspwb 4146 . . 3
31, 2sylib 121 . 2
4 pwexg 4112 . . 3
5 elpwg 3523 . . 3
64, 5syl 14 . 2
73, 6mpbird 166 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wcel 1481  cvv 2689   wss 3076  cpw 3515  cuni 3744 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-14 1493  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4054  ax-pow 4106 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-in 3082  df-ss 3089  df-pw 3517  df-sn 3538  df-uni 3745 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator