Redirect to checkout instead of cart

I have a cart icon in the top navigation bar and when clicked, the page will redirect to checkout instead of the shopping cart page.

My reason is, the shopping cart page contains a table that displays the items added by the customer while the checkout page has the form for billing address and again, the table for displaying the items that are added to cart.

So I came up with the decision to just redirect to checkout instead of cart page to improve convenience and its only redundant if customer's will go to cart page to see their items and then checkout where they can see it also.

Is it a good decision? If not, what is the reason?