Metamath Proof Explorer

Theorem n0i

Description: If a class has elements, then it is not empty. (Contributed by NM, 31-Dec-1993)

Ref Expression
Assertion n0i 
|- ( B e. A -> -. A = (/) )

Proof

Step Hyp Ref Expression
1 noel 
 |-  -. B e. (/)
2 eleq2 
 |-  ( A = (/) -> ( B e. A <-> B e. (/) ) )
3 1 2 mtbiri 
 |-  ( A = (/) -> -. B e. A )
4 3 con2i 
 |-  ( B e. A -> -. A = (/) )