Theorem intv 5370

Description: The intersection of the universal class is empty. (Contributed by NM, 11-Sep-2008.)

Assertion

Ref	Expression
intv	⊢ ∩ V = ∅

Proof of Theorem intv

Step	Hyp	Ref	Expression
1		0ex 5313	. 2 ⊢ ∅ ∈ V
2		int0el 4984	. 2 ⊢ (∅ ∈ V → ∩ V = ∅)
3	1, 2	ax-mp 5	1 ⊢ ∩ V = ∅

Syntax hints:   = wceq 1537   ∈ wcel 2106  Vcvv 3478  ∅c0 4339  ∩ cint 4951

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-nul 5312

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-dif 3966  df-ss 3980  df-nul 4340  df-int 4952

This theorem is referenced by: (None)