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Theorem pwv 4006
 Description: The power class of the universe is the universe. Exercise 4.12(d) of [Mendelson] p. 235. (Contributed by NM, 14-Sep-2003.)
Assertion
Ref Expression
pwv

Proof of Theorem pwv
StepHypRef Expression
1 ssv 3360 . . . 4
2 vex 2951 . . . . 5
32elpw 3797 . . . 4
41, 3mpbir 201 . . 3
54, 22th 231 . 2
65eqriv 2432 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   wcel 1725  cvv 2948   wss 3312  cpw 3791 This theorem is referenced by:  univ  4746  ncanth  6532 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-in 3319  df-ss 3326  df-pw 3793
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