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Theorem elpw2g 3910
 Description: Membership in a power class. Theorem 86 of [Suppes] p. 47. (Contributed by NM, 7-Aug-2000.)
Assertion
Ref Expression
elpw2g

Proof of Theorem elpw2g
StepHypRef Expression
1 elpwi 3368 . 2
2 ssexg 3896 . . . 4
3 elpwg 3367 . . . . 5
43biimparc 283 . . . 4
52, 4syldan 266 . . 3
65expcom 109 . 2
71, 6impbid2 131 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wcel 1393  cvv 2557   wss 2917  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  ax-sep 3875 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:  elpw2  3911  pwnss  3912
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