Hi,giakyI'm not sure that I understand you correctly... You're not sure in your proof?

I'm not sure in correctness of this operation(~p v q) -> (p -> r) transitivity (idk if there is another term?)

Here is my proof. :

[(p -> q) ^ (q -> r)] -> (p -> r)

[(~p v q) ^ (~q v r)] -> (~p v r) ---- by implication

~[(~p v q) ^ (~q v r)] v (~p v r) ---- by implication

[~(~pvq)v~(~qvr)]v(~pvr) --- De Morgan's law

[p^~q)v(q^~r)v(~pvr) --- De Morgan's law

[p^q = pq ----- notation]

[~p='p ----- notation]

p`q v q`r v `p v r ====

now we'll useDistributive Property:x+yz = (x+y) (x+z)

andBasic Identity:x+x’ = 1

p`q v `p = (p v `p)(`q v `p)=`q v `p

q`r v r = (q v r)(`r v r) = q v r

=== `q v `p v q v r = `p v r = p->r

p.s. sorry if there is misunderstanding...I'm just trying to help