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Theorem pweq 3513
 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 3121 . . 3
21abbidv 2257 . 2
3 df-pw 3512 . 2
4 df-pw 3512 . 2
52, 3, 43eqtr4g 2197 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1331  cab 2125   wss 3071  cpw 3510 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-in 3077  df-ss 3084  df-pw 3512 This theorem is referenced by:  pweqi  3514  pweqd  3515  axpweq  4095  pwexg  4104  pwssunim  4206  ordpwsucexmid  4485  fival  6858  istopg  12176  istopon  12190  eltg  12231  tgdom  12251  ntrval  12289
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