Given $a,b,c,d\mathbb\in{R}$ and $a>b$ and $d>c$ how do I prove that $a-c>b-d$?
I started the proof like this: given: $a>b$ I can add to both sides of the ineqality -c therefore I get: $a-c > b-c$
How can I show now that $a-c>b-d$?
Thanks a lot for your time and help.