Can someone please explain how to verify/prove that:

((P => R1) ^ (P => R2)) <=> (P => (R1 ^ R2))

and

((R1 => P) ^ (R2 => P)) <=> ((R1 v R2) => P)

where "^" means "and", "=>" means "implies, and "<=>" means "equivalent to".

They're obviously equivalent from glance, but I just don't know how to mathematically verify them, ie, manipulate left and right sides so that they're identical.

Thanks.