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Theorem nfpw 3402
Description: Bound-variable hypothesis builder for power class. (Contributed by NM, 28-Oct-2003.) (Revised by Mario Carneiro, 13-Oct-2016.)
Hypothesis
Ref Expression
nfpw.1 𝑥𝐴
Assertion
Ref Expression
nfpw 𝑥𝒫 𝐴

Proof of Theorem nfpw
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 df-pw 3392 . 2 𝒫 𝐴 = {𝑦𝑦𝐴}
2 nfcv 2220 . . . 4 𝑥𝑦
3 nfpw.1 . . . 4 𝑥𝐴
42, 3nfss 2993 . . 3 𝑥 𝑦𝐴
54nfab 2224 . 2 𝑥{𝑦𝑦𝐴}
61, 5nfcxfr 2217 1 𝑥𝒫 𝐴
Colors of variables: wff set class
Syntax hints:  {cab 2068  wnfc 2207  wss 2974  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-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  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-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-in 2980  df-ss 2987  df-pw 3392
This theorem is referenced by: (None)
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