If a+c=b+c then a=b

If a+c=b+c then a=b

1 a+c=b+c

2 a+c+(-c)=b+c+(-c)       //add additive inverse of C to both side

3 a+0=b+0                     // additive inverse using 2 

4 a=b                            //additive identity of 3