Please refer to and consider the System Requirements for Premiere Elements 13 Windows
As you may have already noted
2 GHz or faster processor with SSE2 support; dual-core processor required for HDV or AVCHD editing and Blu-ray or AVCHD export; Intel Core i7 required for XAVC-S
What type of projects do you intend to do? I would assume that you would be able to install Premiere Elements 13 on your Windows 7 64 bit computer, but how fast the computer would be able to perform certain task would be in question...but clock speed is not the only processor consideration. Does your computer offer a Turbo Boost feature?
Please consider downloading and installing Premiere Elements 13 on your Windows 7 64 bit computer and determine first hand if the product is compatible with your computer environment and project goals.