Alternating implies flexible

Statement
Suppose $$R$$ is a non-associative ring (i.e., a not necessarily associative ring). Then, if $$R$$ is an alternative ring (i.e., the square of any element is zero) then $$R$$ is a flexible ring.

Facts used

 * 1) uses::Alternating implies skew-commutative
 * 2) uses::Skew-commutative implies flexible