A corollary is that if a given argument is deductively valid, it cannot become invalid by the addition of extra premises.
Monotonicity may be stated formally as a rule called weakening, or sometimes thinning.
The weakening rule may be expressed as a natural deduction sequent: This can be read as saying that if, on the basis of a set of assumptions
This can be weakened by adding a premise: "All men are mortal.
By the property of monotonicity, the argument remains valid with the additional premise, even though the premise is irrelevant to the conclusion.