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Theorem pssv 3507
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 3211 . 2  |-  A  C_  _V
2 dfpss2 3274 . 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 1632   _Vcvv 2801    C_ wss 3165    C. wpss 3166
This theorem is referenced by:  vxveqv  25157
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-ne 2461  df-v 2803  df-in 3172  df-ss 3179  df-pss 3181
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