Theorem

Theorem
Let a,b,c any element of R
a. if a>b and b>c, then a>c
Proof
given a>b and b>c
will be proven a>c
proof
a>b --> a-b Є P .................... Definition 
b>c --> b-c Є P .................... Definition
       (a-b)+(b-c)Є P .............. Definition
 <--> (a+(-b))+(b+(-c))Є P ......... Definition
 <-->  a+((-b)+b)+(-c) Є P ......... Assosiatif
 <-->  a+0+(-c)Є P         ......... Invers
 <-->  a+(-c)Є P           ......... Identitas
 <-->  a - c Є P           ......... Definition
 <-->  a > c                                    ......... Definition
so, Proven that a>c and b>c then a>c