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Theorem intv 5261
 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 5208 . 2 ∅ ∈ V
2 int0el 4905 . 2 (∅ ∈ V → V = ∅)
31, 2ax-mp 5 1 V = ∅
 Colors of variables: wff setvar class Syntax hints:   = wceq 1530   ∈ wcel 2107  Vcvv 3500  ∅c0 4295  ∩ cint 4874 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2798  ax-nul 5207 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2805  df-cleq 2819  df-clel 2898  df-nfc 2968  df-v 3502  df-dif 3943  df-in 3947  df-ss 3956  df-nul 4296  df-int 4875 This theorem is referenced by: (None)
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