Metamath Proof Explorer


Theorem 0sdom

Description: A set strictly dominates the empty set iff it is not empty. (Contributed by NM, 29-Jul-2004)

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

Proof

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