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Theorem pweqb 4422
 Description: Classes are equal if and only if their power classes are equal. Exercise 19 of [TakeutiZaring] p. 18. (Contributed by NM, 13-Oct-1996.)
Assertion
Ref Expression
pweqb

Proof of Theorem pweqb
StepHypRef Expression
1 sspwb 4415 . . 3
2 sspwb 4415 . . 3
31, 2anbi12i 680 . 2
4 eqss 3365 . 2
5 eqss 3365 . 2
63, 4, 53bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   wceq 1653   wss 3322  cpw 3801 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-pw 3803  df-sn 3822  df-pr 3823
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