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

Step	Hyp	Ref	Expression
1		0ex 5308	. 2 ⊢ ∅ ∈ V
2		int0el 4983	. 2 ⊢ (∅ ∈ V → ∩ V = ∅)
3	1, 2	ax-mp 5	1 ⊢ ∩ V = ∅

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)