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Theorem nfpw 3371
 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 3361 . 2 𝒫 𝐴 = {𝑦𝑦𝐴}
2 nfcv 2178 . . . 4 𝑥𝑦
3 nfpw.1 . . . 4 𝑥𝐴
42, 3nfss 2938 . . 3 𝑥 𝑦𝐴
54nfab 2182 . 2 𝑥{𝑦𝑦𝐴}
61, 5nfcxfr 2175 1 𝑥𝒫 𝐴
 Colors of variables: wff set class Syntax hints:  {cab 2026  Ⅎwnfc 2165   ⊆ wss 2917  𝒫 cpw 3359 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-in 2924  df-ss 2931  df-pw 3361 This theorem is referenced by: (None)
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