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Theorem pweqi 4541
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 4540 . 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 1528  𝒫 cpw 4537
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2793
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2800  df-cleq 2814  df-clel 2893  df-in 3942  df-ss 3951  df-pw 4539
This theorem is referenced by:  pwfi  8808  rankxplim  9297  pwdju1  9605  fin23lem17  9749  mnfnre  10673  qtopres  22236  hmphdis  22334  ust0  22757  umgrpredgv  26853  issubgr  26981  uhgrissubgr  26985  cusgredg  27134  cffldtocusgr  27157  konigsbergiedgw  27955  shsspwh  28951  circtopn  31001  lfuhgr  32262  rankeq1o  33530  onsucsuccmpi  33689  elrfi  39171  islmodfg  39549  clsk1indlem4  40274  clsk1indlem1  40275  clsk1independent  40276  omef  42659  caragensplit  42663  caragenelss  42664  carageneld  42665  omeunile  42668  caragensspw  42672  0ome  42692  isomennd  42694  ovn02  42731  lcoop  44364  lincvalsc0  44374  linc0scn0  44376  lincdifsn  44377  linc1  44378  lspsslco  44390  lincresunit3lem2  44433  lincresunit3  44434
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