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Theorem nfpw 3649
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 3640 . 2  |-  ~P A  =  { y  |  y 
C_  A }
2 nfcv 2432 . . . 4  |-  F/_ x
y
3 nfpw.1 . . . 4  |-  F/_ x A
42, 3nfss 3186 . . 3  |-  F/ x  y  C_  A
54nfab 2436 . 2  |-  F/_ x { y  |  y 
C_  A }
61, 5nfcxfr 2429 1  |-  F/_ x ~P A
Colors of variables: wff set class
Syntax hints:   {cab 2282   F/_wnfc 2419    C_ wss 3165   ~Pcpw 3638
This theorem is referenced by:  stoweidlem57  27909
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-in 3172  df-ss 3179  df-pw 3640
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