Within the following axiomatic system :

1) a+b=b+a......................................a.b=b .a

2) (a+b)+c=a+(b+c)................................... .(a.b).c=a(b.c)

3) a+0=a............................................. .......1.a=a

4) a+(-a)=0....................................$\displaystyle a\neq 0\Longrightarrow \frac{1}{a}.a=1$

5) a(b+c)= a.b+a.c

6) $\displaystyle 1\neq 0$

is it possible to have 1+1 =0 ??