PHP mail function doesn't complete sending of e-mail

<?php
    $name = $_POST['name'];
    $email = $_POST['email'];
    $message = $_POST['message'];
    $from = 'From: yoursite.com';
    $to = 'contact@yoursite.com';
    $subject = 'Customer Inquiry';
    $body = "From: $name\n E-Mail: $email\n Message:\n $message";

    if ($_POST['submit']) {
        if (mail ($to, $subject, $body, $from)) {
            echo '<p>Your message has been sent!</p>';
        } else {
            echo '<p>Something went wrong, go back and try again!</p>';
        }
    }
?>

I've tried creating a simple mail form. The form itself is on my index.html page, but it submits to a separate "thank you for your submission" page, thankyou.php, where the above PHP code is embedded. The code submits perfectly, but never sends an email. How can I fix this?