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Theorem intv 4761
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 4712 . 2 ∅ ∈ V
2 int0el 4437 . 2 (∅ ∈ V → V = ∅)
31, 2ax-mp 5 1 V = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1474  wcel 1976  Vcvv 3172  c0 3873   cint 4404
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589  ax-nul 4711
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-v 3174  df-dif 3542  df-in 3546  df-ss 3553  df-nul 3874  df-int 4405
This theorem is referenced by: (None)
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