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Theorem nfpw 3437
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  |-  F/_ x A
Assertion
Ref Expression
nfpw  |-  F/_ x ~P A

Proof of Theorem nfpw
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 df-pw 3427 . 2  |-  ~P A  =  { y  |  y 
C_  A }
2 nfcv 2228 . . . 4  |-  F/_ x
y
3 nfpw.1 . . . 4  |-  F/_ x A
42, 3nfss 3016 . . 3  |-  F/ x  y  C_  A
54nfab 2233 . 2  |-  F/_ x { y  |  y 
C_  A }
61, 5nfcxfr 2225 1  |-  F/_ x ~P A
Colors of variables: wff set class
Syntax hints:   {cab 2074   F/_wnfc 2215    C_ wss 2997   ~Pcpw 3425
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ral 2364  df-in 3003  df-ss 3010  df-pw 3427
This theorem is referenced by: (None)
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