Metamath Proof Explorer

Theorem prnz

Description: A pair containing a set is not empty. (Contributed by NM, 9-Apr-1994)

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

Proof

Step Hyp Ref Expression
1 prnz.1 
 |-  A e. _V
2 1 prid1 
 |-  A e. { A , B }
3 2 ne0ii 
 |-  { A , B } =/= (/)