Metamath Proof Explorer

Theorem 0dom

Description: Any set dominates the empty set. (Contributed by NM, 26-Oct-2003) (Revised by Mario Carneiro, 26-Apr-2015)

Ref Expression
Hypothesis 0sdom.1 
|- A e. _V
Assertion 0dom 
|- (/) ~<_ A

Proof

Step Hyp Ref Expression
1 0sdom.1 
 |-  A e. _V
2 0domg 
 |-  ( A e. _V -> (/) ~<_ A )
3 1 2 ax-mp 
 |-  (/) ~<_ A