Remove 'default.png' when my 'featured-image' class doesn't have a thumbnail.

            <?php
                $thumbnail_id = get_post_thumbnail_id();
                $thumbnail_url= wp_get_attachment_image_src($thumbnail_id, 'thumbnail-size', true);
                $thumbnail_meta = get_post_meta($thumbnail_id, '_wp_attachment_image_alt', true);
            ?>

            <p class="featured-image">
                <img src="<?php echo $thumbnail_url[0]; ?>" alt="<?php echo $thumbnail_meta; ?> featured-image project">
            </p>

This code makes sure that it takes whatever my featured image is on my blog and posts it at the top of each blog. The problem is not all of my blogs have featured images. When there is no featured image given to a post, it displays the 'default.png' file at the top of the page. I could always replace the 'default.png' file with something like my logo, but I wanted to know if I could make it so that if my $thumbnail_url variable doesn't have an image, that it just doesn't put anything there altogether. I can't think of how to write the if statement, and since its already inside the loop, will it break if I add another if statement inside it?

Appreciate the help.