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Theorem intv 4202
Description: The intersection of the universal class is empty. (Contributed by NM, 11-Sep-2008.)
Assertion
Ref Expression
intv  |-  |^| _V  =  (/)

Proof of Theorem intv
StepHypRef Expression
1 0ex 4166 . 2  |-  (/)  e.  _V
2 int0el 3909 . 2  |-  ( (/)  e.  _V  ->  |^| _V  =  (/) )
31, 2ax-mp 8 1  |-  |^| _V  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1632    e. wcel 1696   _Vcvv 2801   (/)c0 3468   |^|cint 3878
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  ax-nul 4165
This theorem depends on definitions:  df-bi 177  df-or 359  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-nfc 2421  df-ne 2461  df-v 2803  df-dif 3168  df-in 3172  df-ss 3179  df-nul 3469  df-int 3879
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