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Theorem pssv 3834
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 3484 . 2  |-  A  C_  _V
2 dfpss2 3550 . 2  |-  ( A 
C.  _V  <->  ( A  C_  _V  /\  -.  A  =  _V ) )
31, 2mpbiran 926 1  |-  ( A 
C.  _V  <->  -.  A  =  _V )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 187    = wceq 1437   _Vcvv 3080    C_ wss 3436    C. wpss 3437
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401
This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-ne 2616  df-v 3082  df-in 3443  df-ss 3450  df-pss 3452
This theorem is referenced by: (None)
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