Hypothetical Syllogism – a logical implication

((P=>Q) ^ (Q => R)) => (P => R) named Hypothetical Syllogism

P => Q (if P imples Q and…)
Q => R (if Q implies R…)
Then, P must imply R.

P = I do not wake up
Q = I cannot go to work.
R = I will not get paid.

If I do not wake up, then I cannot go to work. (P => Q)
If I cannot go to work, then I will not get paid. (Q => R)
Therefore, if I do not wake up, then I will not get paid. (P => R)

3 no namers – logical implications
Hypothetical Syllogism – a logical implication
Disjunctive Syllogism – a logical implication
Simplification – a logical implication
Addition – a logical implication
Modus tollens – a logical implication
Modus ponens – a logical implication
Logical Implications