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Theorem pwexb 4206
 Description: The Axiom of Power Sets and its converse. A class is a set iff its power class is a set. (Contributed by NM, 11-Nov-2003.)
Assertion
Ref Expression
pwexb

Proof of Theorem pwexb
StepHypRef Expression
1 uniexb 4205 . 2
2 unipw 3953 . . 3
32eleq1i 2103 . 2
41, 3bitr2i 174 1
 Colors of variables: wff set class Syntax hints:   wb 98   wcel 1393  cvv 2557  cpw 3359  cuni 3580 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-13 1404  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-un 4170 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-rex 2312  df-v 2559  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-uni 3581 This theorem is referenced by: (None)
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