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Theorem pweqd 3564
Description: Equality deduction for power class. (Contributed by NM, 27-Nov-2013.)
Hypothesis
Ref Expression
pweqd.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
pweqd  |-  ( ph  ->  ~P A  =  ~P B )

Proof of Theorem pweqd
StepHypRef Expression
1 pweqd.1 . 2  |-  ( ph  ->  A  =  B )
2 pweq 3562 . 2  |-  ( A  =  B  ->  ~P A  =  ~P B
)
31, 2syl 14 1  |-  ( ph  ->  ~P A  =  ~P B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1343   ~Pcpw 3559
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 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-11 1494  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147
This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-in 3122  df-ss 3129  df-pw 3561
This theorem is referenced by:  pmvalg  6625  basis1  12685  baspartn  12688  cldval  12739  ntrfval  12740  clsfval  12741  neifval  12780  mopnfss  13087
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