Validity
Here's an argument.
Premise: A if and only if B
Premise: If not quantity A and not R, then quantity A and S
Conclusion: If not quantity B and S, then not quantity A and R
This is a valid argument.
Why, you (probably don't) ask?
Because a process of equivalence, DeMorgan's Theorum, Double Negation, Implication, DeMorgan's, Distribution, Simplification, Simplification, Modus Ponens, Simplification, Conjunction, Distribution, Commutation, Distribution, Simplification, Addition, Association, Implication, DeMorgan's, and Contraposition (in that order) says so.
Premise: A if and only if B
Premise: If not quantity A and not R, then quantity A and S
Conclusion: If not quantity B and S, then not quantity A and R
This is a valid argument.
Why, you (probably don't) ask?
Because a process of equivalence, DeMorgan's Theorum, Double Negation, Implication, DeMorgan's, Distribution, Simplification, Simplification, Modus Ponens, Simplification, Conjunction, Distribution, Commutation, Distribution, Simplification, Addition, Association, Implication, DeMorgan's, and Contraposition (in that order) says so.