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Theorem intv 4375
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 4339 . 2  |-  (/)  e.  _V
2 int0el 4081 . 2  |-  ( (/)  e.  _V  ->  |^| _V  =  (/) )
31, 2ax-mp 8 1  |-  |^| _V  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1652    e. wcel 1725   _Vcvv 2956   (/)c0 3628   |^|cint 4050
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-nul 4338
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-v 2958  df-dif 3323  df-in 3327  df-ss 3334  df-nul 3629  df-int 4051
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