If 1 + 1 ≠ 2 because you are working in the base two system (where 1 + 1 = 10), then 1 still equals 1.
However, if you are working in the base ten system, then since your hypothesis ('let 1 + 1 ≠ 2') is false, you can write anything for your conclusion. The statement may be complete nonsense, but the full statement won't be false.
If 1 + 1 ≠ 2 because you are working in the base two system (where 1 + 1 = 10), then 1 still equals 1.
However, if you are working in the base ten system, then since your hypothesis ('let 1 + 1 ≠ 2') is false, you can write anything for your conclusion. The statement may be complete nonsense, but the full statement won't be false.