Metamath Proof Explorer

Theorem intv

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

Ref Expression
Assertion intv 
|- |^| _V = (/)

Proof

Step Hyp Ref Expression
1 0ex 
 |-  (/) e. _V
2 int0el 
 |-  ( (/) e. _V -> |^| _V = (/) )
3 1 2 ax-mp 
 |-  |^| _V = (/)