Metamath Proof Explorer


Theorem 1n0OLD

Description: Obsolete version of 1n0 as of 10-Jun-2026. (Contributed by NM, 26-Dec-2004) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion 1n0OLD
|- 1o =/= (/)

Proof

Step Hyp Ref Expression
1 df1o2
 |-  1o = { (/) }
2 0ex
 |-  (/) e. _V
3 2 snnz
 |-  { (/) } =/= (/)
4 1 3 eqnetri
 |-  1o =/= (/)