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Theorem pweqi 3568
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 3567 . 2  |-  ( A  =  B  ->  ~P A  =  ~P B
)
31, 2ax-mp 5 1  |-  ~P A  =  ~P B
Colors of variables: wff set class
Syntax hints:    = wceq 1348   ~Pcpw 3564
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 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-in 3127  df-ss 3134  df-pw 3566
This theorem is referenced by:  exmidpw  6884  exmidpweq  6885  pw1dom2  7197  pw1ne1  7199  mnfnre  7955  fmelpw1o  13806
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