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Theorem pweqi 3518
 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 3517 . 2 (𝐴 = 𝐵 → 𝒫 𝐴 = 𝒫 𝐵)
31, 2ax-mp 5 1 𝒫 𝐴 = 𝒫 𝐵
 Colors of variables: wff set class Syntax hints:   = wceq 1332  𝒫 cpw 3514 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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-in 3081  df-ss 3088  df-pw 3516 This theorem is referenced by:  exmidpw  6809  mnfnre  7831  pw1dom2  13359
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