Theorem intv 5325

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 5260	. 2 ⊢ ∅ ∈ V
2		int0el 4938	. 2 ⊢ (∅ ∈ V → ∩ V = ∅)
3	1, 2	ax-mp 5	1 ⊢ ∩ V = ∅

This proof depends on syntax axioms:   = wceq 1569   ∈ wcel 2144  Vcvv 3450  ∅c0 4278  ∩ cint 4906

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732  ax-nul 5259

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-ss 3896  df-dif 4047  df-nul 4279  df-int 4907

This theorem is used by: (None)