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Theorem intv 5364
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 5308 . 2 ∅ ∈ V
2 int0el 4983 . 2 (∅ ∈ V → V = ∅)
31, 2ax-mp 5 1 V = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  wcel 2098  Vcvv 3461  c0 4322   cint 4950
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 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696  ax-nul 5307
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-v 3463  df-dif 3947  df-ss 3961  df-nul 4323  df-int 4951
This theorem is referenced by: (None)
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