Metamath Proof Explorer

Theorem tpnz

Description: An unordered triple containing a set is not empty. (Contributed by NM, 10-Apr-1994)

Ref Expression
Hypothesis tpnz.1 
|- A e. _V
Assertion tpnz 
|- { A , B , C } =/= (/)

Proof

Step Hyp Ref Expression
1 tpnz.1 
 |-  A e. _V
2 1 tpid1 
 |-  A e. { A , B , C }
3 2 ne0ii 
 |-  { A , B , C } =/= (/)