Metamath Proof Explorer

Theorem 0ellim

Description: A limit ordinal contains the empty set. (Contributed by NM, 15-May-1994)

Ref Expression
Assertion 0ellim 
|- ( Lim A -> (/) e. A )

Proof

Step Hyp Ref Expression
1 dflim2 
 |-  ( Lim A <-> ( Ord A /\ (/) e. A /\ A = U. A ) )
2 1 simp2bi 
 |-  ( Lim A -> (/) e. A )