Theorem intv 5362

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 5307	. 2 ⊢ ∅ ∈ V
2		int0el 4983	. 2 ⊢ (∅ ∈ V → ∩ V = ∅)
3	1, 2	ax-mp 5	1 ⊢ ∩ V = ∅

Syntax hints:   = wceq 1542   ∈ wcel 2107  Vcvv 3475  ∅c0 4322  ∩ cint 4950

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-nul 5306

This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-dif 3951  df-in 3955  df-ss 3965  df-nul 4323  df-int 4951

This theorem is referenced by: (None)