Metamath Proof Explorer

Theorem nel02

Description: The empty set has no elements. (Contributed by Peter Mazsa, 4-Jan-2018)

Ref Expression
Assertion nel02 
|- ( A = (/) -> -. B e. 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 )