Below is a quick overview of Yahoo! and it’s Search History, so you can see that they have in the past used Google.
In May of 1998, Yahoo! Web Search is powered by Inktomi
In June of 2000, Yahoo! Web Search powered by Google
In March of 2003, Yahoo! Acquires Inktomi
In February of 2004 Yahoo! Web Search powered by Yahoo!
In March of 2004 AltaVista switches to Yahoo! Search
In August of 2004 Yahoo! Launches Local Search Engine
On August 18th 2010 Yahoo switches to BING
Yahoo! Organic Results Switch To Bing (Aug 18th, 2010)
Yahoo Outsource Search to Google! Today WSJ
Yahoo Layoffs Confirmed (Monday Jan 21st 2008)
Yahoo Layoffs Updated (Tuesday Jan 22nd 2008)