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Theorem pweqd 3481
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 3479 . 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 1314  𝒫 cpw 3476
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-11 1467  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-in 3043  df-ss 3050  df-pw 3478
This theorem is referenced by:  pmvalg  6507  basis1  12057  baspartn  12060  cldval  12111  ntrfval  12112  clsfval  12113  neifval  12152  mopnfss  12436
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