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Theorem pweqi 3629
Description: Equality inference for power class. (Contributed by NM, 27-Nov-2013.)
Hypothesis
Ref Expression
pweqi.1  |-  A  =  B
Assertion
Ref Expression
pweqi  |-  ~P A  =  ~P B

Proof of Theorem pweqi
StepHypRef Expression
1 pweqi.1 . 2  |-  A  =  B
2 pweq 3628 . 2  |-  ( A  =  B  ->  ~P A  =  ~P B
)
31, 2ax-mp 8 1  |-  ~P A  =  ~P B
Colors of variables: wff set class
Syntax hints:    = wceq 1623   ~Pcpw 3625
This theorem is referenced by:  pwfi  7151  rankxplim  7549  pwcda1  7820  fin23lem17  7964  mnfnre  8875  qtopres  17389  hmphdis  17487  shsspwh  21825  rankeq1o  24801  onsucsuccmpi  24882  selsubf  25990  selsubf3  25991  elrfi  26769  islmodfg  27167
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-in 3159  df-ss 3166  df-pw 3627
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