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Theorem pweqi 3795
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 3794 . 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 1652   ~Pcpw 3791
This theorem is referenced by:  pwfi  7394  rankxplim  7793  pwcda1  8064  fin23lem17  8208  mnfnre  9118  qtopres  17720  hmphdis  17818  ust0  18239  shsspwh  22738  rankeq1o  26077  onsucsuccmpi  26158  elrfi  26702  islmodfg  27099
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-in 3319  df-ss 3326  df-pw 3793
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