Theorem pweqi 4354

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

Step	Hyp	Ref	Expression
1		pweqi.1	. 2 ⊢ 𝐴 = 𝐵
2		pweq 4353	. 2 ⊢ (𝐴 = 𝐵 → 𝒫 𝐴 = 𝒫 𝐵)
3	1, 2	ax-mp 5	1 ⊢ 𝒫 𝐴 = 𝒫 𝐵

Syntax hints:   = wceq 1653  𝒫 cpw 4350

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-ext 2778

This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2787  df-cleq 2793  df-clel 2796  df-in 3777  df-ss 3784  df-pw 4352

This theorem is referenced by:  pwfi  8504  rankxplim  8993  pwcda1  9305  fin23lem17  9449  mnfnre  10372  qtopres  21829  hmphdis  21927  ust0  22350  umgrpredgv  26375  issubgr  26504  uhgrissubgr  26508  cusgredg  26673  cffldtocusgr  26696  konigsbergiedgw  27594  shsspwh  28627  circtopn  30419  rankeq1o  32790  onsucsuccmpi  32949  elrfi  38038  islmodfg  38419  clsk1indlem4  39119  clsk1indlem1  39120  clsk1independent  39121  omef  41451  caragensplit  41455  caragenelss  41456  carageneld  41457  omeunile  41460  caragensspw  41464  0ome  41484  isomennd  41486  ovn02  41523  lcoop  42994  lincvalsc0  43004  linc0scn0  43006  lincdifsn  43007  linc1  43008  lspsslco  43020  lincresunit3lem2  43063  lincresunit3  43064