Another consequence is that exponentiation a^b can be considered the same thing as b -> a.
In the case where a and b are not strictly boolean (supposing they are instead probabilities for example) you could even generalize it somewhat in terms of "pure" mathematical operations.
double implies(double a, double b) {
double dif = a - b;
double abx = sqrt(dif * dif);
return 1 + pow(0, abx - dif) - pow(1, abx + dif);
}