see below.
The Law of Detachment states that if the two statements are true:
If ##p##, then ##q##
##p##
then we can conclude a third statement ====>##q##
Example:
If the whale is a mammal (##p##), then it has teats (##q##).
The whale is a mammal (##p##).
Conclusion: The whale has teats (##q##).
The Law of Syllogism states that if one thing implies the second, and the second implies the third, then we can conclude that the first implies the third.
If ##p##, then ##q##.
If ##q##, then ##r##
Conclusion: ##p##, therefore ##r##.
Example:
If Leah is intelligent (##p##), then she is an honor pupil (##q##).
If she is an honor pupil (##q##), then she is under a scholarship grant (##r##).
Conclusion:
Leah is intelligent (##p##), therefore she is under a scholarship grant (##r##).