Theorem pweqi 4563

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 4561	. 2 ⊢ (𝐴 = 𝐵 → 𝒫 𝐴 = 𝒫 𝐵)
3	1, 2	ax-mp 5	1 ⊢ 𝒫 𝐴 = 𝒫 𝐵

Syntax hints:   = wceq 1540  𝒫 cpw 4547

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 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2707

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-v 3443  df-in 3905  df-ss 3915  df-pw 4549

This theorem is referenced by:  pwfiOLD  9212  rankxplim  9736  pwdju1  10047  fin23lem17  10195  mnfnre  11119  qtopres  22955  hmphdis  23053  ust0  23477  umgrpredgv  27799  issubgr  27927  uhgrissubgr  27931  cusgredg  28080  cffldtocusgr  28103  konigsbergiedgw  28900  shsspwh  29896  circtopn  32085  lfuhgr  33378  made0  34153  rankeq1o  34569  onsucsuccmpi  34728  bj-unirel  35335  elrfi  40786  islmodfg  41165  clsk1indlem4  41984  clsk1indlem1  41985  clsk1independent  41986  omef  44380  caragensplit  44384  caragenelss  44385  carageneld  44386  omeunile  44389  caragensspw  44393  0ome  44413  isomennd  44415  ovn02  44452  lcoop  46112  lincvalsc0  46122  linc0scn0  46124  lincdifsn  46125  linc1  46126  lspsslco  46138  lincresunit3lem2  46181  lincresunit3  46182