Theorem intv 5311

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 5254	. 2 ⊢ ∅ ∈ V
2		int0el 4936	. 2 ⊢ (∅ ∈ V → ∩ V = ∅)
3	1, 2	ax-mp 5	1 ⊢ ∩ V = ∅

Syntax hints:   = wceq 1542   ∈ wcel 2114  Vcvv 3442  ∅c0 4287  ∩ cint 4904

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-nul 5253

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-v 3444  df-dif 3906  df-ss 3920  df-nul 4288  df-int 4905

This theorem is referenced by: (None)