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Theorem nfpw 3579
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 3568 . 2 𝒫 𝐴 = {𝑦𝑦𝐴}
2 nfcv 2312 . . . 4 𝑥𝑦
3 nfpw.1 . . . 4 𝑥𝐴
42, 3nfss 3140 . . 3 𝑥 𝑦𝐴
54nfab 2317 . 2 𝑥{𝑦𝑦𝐴}
61, 5nfcxfr 2309 1 𝑥𝒫 𝐴
Colors of variables: wff set class
Syntax hints:  {cab 2156  wnfc 2299  wss 3121  𝒫 cpw 3566
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-ral 2453  df-in 3127  df-ss 3134  df-pw 3568
This theorem is referenced by: (None)
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