Metamath Proof Explorer


Theorem 0nnnALT

Description: Alternate proof of 0nnn , which requires ax-pre-mulgt0 but is not based on nnne0 (and which can therefore be used in nnne0ALT ). (Contributed by NM, 25-Aug-1999) (New usage is discouraged.) (Proof modification is discouraged.)

Ref Expression
Assertion 0nnnALT
|- -. 0 e. NN

Proof

Step Hyp Ref Expression
1 0lt1
 |-  0 < 1
2 nnnlt1
 |-  ( 0 e. NN -> -. 0 < 1 )
3 1 2 mt2
 |-  -. 0 e. NN