Deductive arguments do not repeat premises.
Based upon the examples in your post, it appears we disagree on what it means to repeat premises.
You are saying apples are red, blood is red, therefore apples and blood are red.
Yeah, no. I made a much larger claim.
The apple/blood claim:
Circle R contains circle A
Circle R contains circle B
Therefore circle R contains circle A and circle B
A valid but boring deductive argument demonstrating the distribution of AND and IF. (IF A) and (IF B) = IF (A and B)
My claim:
Circle P is contained within circle B
Circle R is overlaps some of circle P
Therefore there is a section of circle P that overlaps circle R and circle B (Note the claim that R and B overlap)
A valid and more complex deductive argument.
What I did was used circle P to describe some of the relationship between circles B and R. Namely that they overlap within a section of circle P.