# Where does the CPA come from?

Mr. Nance,

I’m stumped on Logic lesson 18 #5. We got same answers as answer key until line 7…I can see from line 8 why line 7 is important, but how did we deduce a consequent that was not the original consequent of line 1 (from which we assumed the antecedent in line 3)?

Hope that makes sense!

You appear to have a fundamental misconception about conditional proof. It’s a common error in thinking that the assumed antecedent “comes from” a previous step in the proof. This misconception is evident when you say “line 1 (from which we assumed the antecedent in line 3).” But in actuality, you do not assume the antecedent from line 1. In a conditional proof, you assume the antecedent out of thin air (like I say in the video). You can get an idea of what you need to assume by looking at the premises and conclusion of the proof, but the assumption does not come from there. You quite simply assume the antecedent.

You also ask, “how did we deduce a consequent that was not the original consequent of line 1”? The only answer is that we deduced it from the conditional proof assumption and the other steps in the proof. But the consequent deduced does not need to come from any previous step. I tried to show this idea in my example from the middle of page 139. You can use conditional proof even when the conclusion is not a conditional.

I hope this makes sense!