You can find the definition of ice cream in the Code of Federal Regulations (CFR) Title 21, Chapter 1, Subchapter B, Part 135, subpart B. "Requirements for specific standardized frozen desserts".
It is not "ice cream for ice cream", it is supposed to sound like that but it is actually "I scream for ice cream". The phrase is derived from a popular 1927 song titled "I Scream, You Scream, We All...