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Theorem pweqb 4124
 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 4117 . . 3
2 sspwb 4117 . . 3
31, 2anbi12i 681 . 2
4 eqss 3115 . 2
5 eqss 3115 . 2
63, 4, 53bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   wceq 1619   wss 3078  cpw 3530 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-sep 4038  ax-nul 4046  ax-pr 4108 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-v 2729  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-pw 3532  df-sn 3550  df-pr 3551
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