Aid solving logical puzzle I have a logical puzzle here that I need to solve. I'm not after just the answer of this puzzle, but also the reasoning and thought-process behind solving it. Any assistance is greatly appreciated.

What number between 1 and 7 do the following equal? A=, B=, C=, D=, E=, F=, G=

Given that:

1.  A ≠ 2 
2.  A + B = F 
3.  C – D = G 
4.  D + E = 2F 
5.  E + G = F 


The rules are: 

1. All the variables (A, B, C, D, E, F, G) are equal to integer values between 1 and 7 
2. None of the variables (A, B, C, D, E, F, G) are equal to each other i.e. all seven values will be used, no repeat use of integers
Notice that if you have positive numbers, the relation $x+y=z$ implies $x&lt;z$ and $y&lt;z$. So properties 2., 3., 5. give $A&lt;F$, $B&lt;F$, $D&lt;C$, $G&lt;C$, $E&lt;F$, $G&lt;F$. 
Moreover since $D+E = 2F$ and $E&lt;F$ you get $F&lt;D$.
So $A,B,E,G &lt; F &lt; D &lt; C$ which means that $F = 5, D = 6, C = 7$.

Then from 4. $E=4$, from 3. $G=1$ from 1. $A=3$, $B=2$.
$A = 3, B = 2, C = 7, D=6, E = 4, F = 5, G=1$