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Theorem pweqi 4533
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 4531 . 2 (𝐴 = 𝐵 → 𝒫 𝐴 = 𝒫 𝐵)
31, 2ax-mp 5 1 𝒫 𝐴 = 𝒫 𝐵
Colors of variables: wff setvar class
Syntax hints:   = wceq 1537  𝒫 cpw 4515
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2792
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-clab 2799  df-cleq 2813  df-clel 2891  df-nfc 2959  df-v 3475  df-in 3920  df-ss 3930  df-pw 4517
This theorem is referenced by:  pwfi  8797  rankxplim  9286  pwdju1  9594  fin23lem17  9738  mnfnre  10662  qtopres  22282  hmphdis  22380  ust0  22804  umgrpredgv  26912  issubgr  27040  uhgrissubgr  27044  cusgredg  27193  cffldtocusgr  27216  konigsbergiedgw  28012  shsspwh  29008  circtopn  31112  lfuhgr  32372  rankeq1o  33640  onsucsuccmpi  33799  bj-unirel  34361  elrfi  39428  islmodfg  39806  clsk1indlem4  40529  clsk1indlem1  40530  clsk1independent  40531  omef  42926  caragensplit  42930  caragenelss  42931  carageneld  42932  omeunile  42935  caragensspw  42939  0ome  42959  isomennd  42961  ovn02  42998  lcoop  44611  lincvalsc0  44621  linc0scn0  44623  lincdifsn  44624  linc1  44625  lspsslco  44637  lincresunit3lem2  44680  lincresunit3  44681
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