solakis1
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Given for all A,B,C...
1) A+B=B+A......AB=BA
2) A+(B+C)=(A+B)+C.......A(BC)=(AB)C
3) A+0=A..........1A=A
4) $$\forall A\exists B(A+B=0)$$.....$$\forall A(\neg(A=0)\Longrightarrow\exists B(AB=1))$$
5) A(B+C)= AB+AC
Then prove: $$AA=BB\Longrightarrow (A+B)=0\vee A=B$$
Note: AB means A.B ...e.t.c ,e.t.c
1) A+B=B+A......AB=BA
2) A+(B+C)=(A+B)+C.......A(BC)=(AB)C
3) A+0=A..........1A=A
4) $$\forall A\exists B(A+B=0)$$.....$$\forall A(\neg(A=0)\Longrightarrow\exists B(AB=1))$$
5) A(B+C)= AB+AC
Then prove: $$AA=BB\Longrightarrow (A+B)=0\vee A=B$$
Note: AB means A.B ...e.t.c ,e.t.c