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Theorem pweq 3354
 Description: Equality theorem for power class. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
pweq

Proof of Theorem pweq
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sseq2 2961 . . 3
21abbidv 2152 . 2
3 df-pw 3353 . 2
4 df-pw 3353 . 2
52, 3, 43eqtr4g 2094 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1242  cab 2023   wss 2911  cpw 3351 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-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-ss 2925  df-pw 3353 This theorem is referenced by:  pweqi  3355  pweqd  3356  axpweq  3915  pwex  3923  pwexg  3924  pwssunim  4012  ordpwsucexmid  4246
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