Brevity motivates abbreviation Conditional Proof as CP, Conditional Statements as CS, and Indirect Proof as IS.
Source: A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley
[ p 437, Chapter 7.5 'Conditional Proof' ]
Conditional proof may thus be seen as completing the rules of inference. The method consists of assuming the antecedent of the required conditional statement on one line, deriving the consequent on a subsequent line, and then “discharging” this sequence of lines in a conditional statement that exactly replicates the one that was to be obtained.
[ p 446, Chapter 7.6 'Indirect Proof' ]
This example illustrates how a conditional proof can be used to derive the conclusion of any argument, whether or not the conclusion is a conditional statement. Simply begin by assuming the negation of the conclusion, derive contradictory statements on separate lines, and use these lines to set up a disjunctive syllogism yielding the negation of the assumption as the last line of the conditional sequence. Then, discharge the sequence and use tautology to derive the negation of the assumption outside the sequence.
Because both paragraphs above discuss the same CP, should they cohere with each other 100%? If not, does each logically imply the other? I am confused if the differences cannot be conciliated.
To me, the two quoted paragraphs appear different because
(from p 437) assuming the antecedent of the required conditional statement
differs from (p 446) assuming the negation of the conclusion
(this last bolded phrase says nothing about CS). To wit, an IP's conclusion may NOT be a CS.. In fact, the example referenced in p 446's conclusion is ~A, which is NOT a CS.