Convert a substitution rule into an equation

Questions
1

Dear community,

Newbie here. I would like to convert the results of a solve function into an equation; that is, go from this: {a-> b/3}, to this: a==b/3.
It seems that conversion in the opposite direction is possible with the ToRules command, but how to go in the other way?

Thanks
Zhao

2

In[1]:= rule = (x_ → y_) → (x == y)

Out[1]= (x_ -> y_) -> x == y

In[2]:= a -> b /. rule

Out[2]= a == b

In[3]:= {a -> b, c -> d} /. rule

Out[3]= {a == b, c == d}
3

or :

In[1]:= {a -> b, c -> d} /. Rule -> Equal

Out[1]= {a == b, c == d}