Thanks for the question! So a subsidiary conclusion is basically a conclusion that is both a conclusion and a premise. In other words, it goes on to support the main conclusion, but is itself supported by other premises. So take the following argument:
It’s wet outside. That means it must’ve rained. If it rained, I don’t need to turn on my sprinklers. Therefore, I can turn my sprinklers off.
Here, we know the first sentence “it’s wet outside” is just a premise, a fact/statement that’s asserted. The next sentence is “That means it must’ve rained,” and this is an intermediate/subsidiary conclusion. How do we know it must’ve rained? Well, because it’s wet outside! So the first premise supports this statement, which automatically makes it a conclusion of some kind. But it’s not the main conclusion here—the main conclusion is the last statement, that I can turn my sprinklers off. And we know I can turn my sprinklers off because it rained, and if it rained, I don’t need to turn them on. So the second statement goes on to support the last statement. And that’s the essence of a subsidiary conclusion.
Hope this helps! Feel free to ask any other questions that you might have.