Question about logic implications If $X\implies Y$ and $X\implies Z$, does that mean that $Y\implies Z$?
I think it does, but can anyone show this as a proof?
Thanks

No. 
What is true is $$[(X \rightarrow Y) \land (X \rightarrow Z)]\implies (X \rightarrow (Y \land Z))$$
In the case that you know $$(X\rightarrow Y) \land (Y\rightarrow Z),$$ then you can infer $$X \rightarrow Z.$$
