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Theorem pweqi 3748
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 3747 . 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 1649   ~Pcpw 3744
This theorem is referenced by:  pwfi  7339  rankxplim  7738  pwcda1  8009  fin23lem17  8153  mnfnre  9063  qtopres  17653  hmphdis  17751  ust0  18172  shsspwh  22598  rankeq1o  25828  onsucsuccmpi  25909  elrfi  26441  islmodfg  26838
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2370
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2376  df-cleq 2382  df-clel 2385  df-in 3272  df-ss 3279  df-pw 3746
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