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Theorem nfpw 3518
 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 3507 . 2 𝒫 𝐴 = {𝑦𝑦𝐴}
2 nfcv 2279 . . . 4 𝑥𝑦
3 nfpw.1 . . . 4 𝑥𝐴
42, 3nfss 3085 . . 3 𝑥 𝑦𝐴
54nfab 2284 . 2 𝑥{𝑦𝑦𝐴}
61, 5nfcxfr 2276 1 𝑥𝒫 𝐴
 Colors of variables: wff set class Syntax hints:  {cab 2123  Ⅎwnfc 2266   ⊆ wss 3066  𝒫 cpw 3505 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-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ral 2419  df-in 3072  df-ss 3079  df-pw 3507 This theorem is referenced by: (None)
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