Metamath Proof Explorer


Theorem leneg

Description: Negative of both sides of 'less than or equal to'. (Contributed by NM, 12-Sep-1999) (Proof shortened by Mario Carneiro, 27-May-2016)

Ref Expression
Assertion leneg ABABBA

Proof

Step Hyp Ref Expression
1 0re 0
2 lesub2 AB0AB0B0A
3 1 2 mp3an3 ABAB0B0A
4 df-neg B=0B
5 df-neg A=0A
6 4 5 breq12i BA0B0A
7 3 6 bitr4di ABABBA