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Theorem pweqd 3395
 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 3393 . 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 1285  𝒫 cpw 3390 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-in 2980  df-ss 2987  df-pw 3392 This theorem is referenced by: (None)
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