For example: premise A→B, B→C, conclusion A → C.

Prove:

(1) A P (annex)

(2) A → B

B T( 1)(2)I

(4)B→C P

(5) Item 1, Paragraph 4, Article 3 of the Council of Europe Treaty.

(6)A→C CP

When proved by the reduction to absurdity.

Premise a, A→B, conclusion b

Prove:

(1)┐B P (annex)

(2) A → B

(3)┐B→┐A T(2)E

(4)┐A T( 1)(3)I

(5) a PI

(6) A contradiction of ∧ ┐A T(4)(5)