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Theorem pssv 3660
Description: Any non-universal class is a proper subclass of the universal class. (Contributed by NM, 17-May-1998.)
Assertion
Ref Expression
pssv  |-  ( A 
C.  _V  <->  -.  A  =  _V )

Proof of Theorem pssv
StepHypRef Expression
1 ssv 3361 . 2  |-  A  C_  _V
2 dfpss2 3425 . 2  |-  ( A 
C.  _V  <->  ( A  C_  _V  /\  -.  A  =  _V ) )
31, 2mpbiran 885 1  |-  ( A 
C.  _V  <->  -.  A  =  _V )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 177    = wceq 1652   _Vcvv 2949    C_ wss 3313    C. wpss 3314
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 2417
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-ne 2601  df-v 2951  df-in 3320  df-ss 3327  df-pss 3329
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