1. Mickey Mouse exists (as a real flesh and blood individual).
2. Mickey Mouse wears pants and drives a car.
3. I exist (as a real flesh and blood individual).
4. I wear pants and drive a car.
5. If 4 is true, then 1 is true and MM really exists.
Or:
1. Rabbits have eight legs.
2. Rabbits are members of the animal kingdom.
3. Octopi have eight legs.
4. Octopi are members of the animal kingdom.
5. If 4 is true, then 1 is true and rabbits have eight legs.
Analogies do not prove anything; they merely help to comprehend a concept or event by comparing it to something more familiar that has a few key corresponding attributes. Other attributes that are not comparable, such as divinity or omniscience, keep the analogy from actually PROVING anything about the subject. If this were not true, then your 'logic' would DISPROVE the trinity since water actually has many more than tree states! You left off the plasma state (and several other ionized states) and the fact that ice has many distinct crystal forms. So there wouldn't be a Trinity, but a Dodecatinity, or something.