It depends on how visible your child navigation is. While Breadcrumbs can be redundant in some cases, they do serve as a medium of quick navigation as well.
To quote this article Breadcrumb Navigation Examined: Best Practices & Examples
Fact of the matter is, breadcrumb navigation will greatly increase the usability of a website. Breadcrumbs give users an alternative method of navigation, allow them to see where they stand in the hierarchy of a website, and will reduce the number of steps needed to navigate to a higher-level within a website.
This article from smashing Magazine Breadcrumbs In Web Design: Examples And Best Practices has this to say :
Here are just some of the benefits of using a breadcrumb trail.
Convenient for users Breadcrumbs are used primarily to give users a secondary means of navigating a website. By offering a breadcrumb trail for all pages on a large multi-level website, users can navigate to higher-level categories more easily.
Reduces clicks or actions to return to higher-level pages
Instead of using the browser’s “Back” button or the website’s primary navigation to return to a higher-level page, users can now use the breadcrumbs with a fewer number of clicks.
Doesn’t usually hog screen space.
Because they’re typically horizontally oriented and plainly styled, breadcrumb trails don’t take up a lot of space on the page. The benefit is that they have little to no negative impact in terms of content overload, and they outweigh any negatives if used properly.
Reduces bounce rates Breadcrumb trails can be a great way to entice first-time visitors to peruse a website after having viewed the landing page. For example, say a user arrives on a page through a Google search, seeing a breadcrumb trail may tempt that user to click to higher-level pages to view related topics of interests. This, in turn, reduces the overall website bounce rate.