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Theorem pssv 3603
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 3304 . 2  |-  A  C_  _V
2 dfpss2 3368 . 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 1649   _Vcvv 2892    C_ wss 3256    C. wpss 3257
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-ne 2545  df-v 2894  df-in 3263  df-ss 3270  df-pss 3272
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