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Theorem pweqd 3548
 Description: Equality deduction for power class. (Contributed by NM, 27-Nov-2013.)
Hypothesis
Ref Expression
pweqd.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
pweqd (𝜑 → 𝒫 𝐴 = 𝒫 𝐵)

Proof of Theorem pweqd
StepHypRef Expression
1 pweqd.1 . 2 (𝜑𝐴 = 𝐵)
2 pweq 3546 . 2 (𝐴 = 𝐵 → 𝒫 𝐴 = 𝒫 𝐵)
31, 2syl 14 1 (𝜑 → 𝒫 𝐴 = 𝒫 𝐵)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1335  𝒫 cpw 3543 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 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-11 1486  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-in 3108  df-ss 3115  df-pw 3545 This theorem is referenced by:  pmvalg  6601  basis1  12416  baspartn  12419  cldval  12470  ntrfval  12471  clsfval  12472  neifval  12511  mopnfss  12818
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