This is explained on slides 81-83 of the temporal logic chapter. The point is that we can neglect the fairness constraint for positive occurrences of [φ WU ψ] we can neglect the fairness constraint for negative occurrences of [φ SU ψ] and that carries over to the other operators that are defined as syntactic sugar. As Fψ is defined as [true SU ψ], we can neglect the fairness constraint for negative occurrences of Fψ. The occurrences of the operators F U and G in the formula are all behind a negation, so they are all negative occurrences. Hence, we can omit the fairness constraint of the F operator (but adding it is also correct).
