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Theorem nfpw 3733
 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 xA

Proof of Theorem nfpw
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 df-pw 3724 . 2 A = {y y A}
2 nfcv 2489 . . . 4 xy
3 nfpw.1 . . . 4 xA
42, 3nfss 3266 . . 3 x y A
54nfab 2493 . 2 x{y y A}
61, 5nfcxfr 2486 1 xA
 Colors of variables: wff setvar class Syntax hints:  {cab 2339  Ⅎwnfc 2476   ⊆ wss 3257  ℘cpw 3722 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-pw 3724 This theorem is referenced by: (None)
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