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Theorem pssv 3494
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 3198 . 2  |-  A  C_  _V
2 dfpss2 3261 . 2  |-  ( A 
C.  _V  <->  ( A  C_  _V  /\  -.  A  =  _V ) )
31, 2mpbiran 884 1  |-  ( A 
C.  _V  <->  -.  A  =  _V )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    = wceq 1623   _Vcvv 2788    C_ wss 3152    C. wpss 3153
This theorem is referenced by:  vxveqv  25054
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-ne 2448  df-v 2790  df-in 3159  df-ss 3166  df-pss 3168
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