Choose from a drop down list only if it hasn't been chosen previously in different column

Hi, I would appreciate some help with this. I have looked for this online but couldn't find any that sorted this issue.

I am looking to set up a number of colums with drop down menus. However, if an option has been chosen in the previous column (or columns) I want it NOT to be available in subsequent columns;

For example;

- In the first column the drop down choices would be; Mouse, Cat, Dog, Horse, Bear
- I choose Dog in the first column.
- I want the second column to only give me the drop down choices of; Mouse, Cat, Horse, Bear. (I.E. Dog has now been removed from the drop down list).
- I then choose Bear in the second column
- I want the third column to only give me the drop down choices of; Mouse Cat Horse (I.E. Both Dog and Bear have now been removed from the drop down list).

I should add that there will be a number of rows. So Person A may choose Dog while Person B may choose Cat in the first column. Therefore Person A does not have Dog as a choice in the second column but can choose any of the others. Person B does not have Cat but can choose any of the others.

I hope I have explained that ok and thanks.

Thanks Whizbang. That's great and certainly getting there.

I just wonder if rather than setting up different list columns and named ranges for each row there was a way to account for it in the formula for first row that automatically identifies choices in the subsequent rows too. Probably not. I'll keep digging away at it.