Let x = set of natural numbers.
EQUAL(X,Y) : 'X' is equal to 'Y'
EVEN(X) : 'X' is even.
PRIME(X) : 'X' is prime.
"The only even prime is "2" can be expressed as :
∀x [ (EVEN(X) ∧ PRIME(X)) ↔ EQUAL(X,2)]
Here bi-direction is necessary because if only uni-direction implication were there from Left to Right and consider if number is even but prime ,so LHS becomes false so we can't say anything about RHS i.e whether number is two or not.This is so because in implication,if LHS is false we can't say anything about RHS and whole implication becomes true i.e F -> T or F is always true.
Hence we need both side implication to show that if given no. is both prime and even then it is only '2' ,and if given no. is '2' then its even & prime both.
I hope it clear many doubts related to implication.