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Theorem intv 5033
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 4984 . 2 ∅ ∈ V
2 int0el 4698 . 2 (∅ ∈ V → V = ∅)
31, 2ax-mp 5 1 V = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1653  wcel 2157  Vcvv 3385  c0 4115   cint 4667
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-13 2377  ax-ext 2777  ax-nul 4983
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2786  df-cleq 2792  df-clel 2795  df-nfc 2930  df-v 3387  df-dif 3772  df-in 3776  df-ss 3783  df-nul 4116  df-int 4668
This theorem is referenced by: (None)
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