I have been trying to figure out(prove) Goldbach Conjecture(Strong) which states: Every even integer greater than 2 can be expressed as the sum of two primes. My question I guess is general, is it wrong for me to prove something using "simple statements". Here are my statements:
Every prime number greater than 2 is odd. Every even integer is the sum of two odd numbers. Therefore, the conjecture is true.
In math, is it not allowed to make general statements OR must I prove this by other means like for example, proof by contradiction, direct proof etc.?