I am very new to logic and currently taking a course about it but unfortunately it's a weekend now so I can't get the answers I need!
Basically I am wondering a very basic thing. I want to prove something with natural deduction and let's say I have this premise:
Ok so let's start the question, here's an example but not a full example, just a short bit:
$\forall x\forall y\big(A(x)\to B(y)\big)\qquad\text{(premise)}$
So we got these two variables $x$ and $y$ and then just get rid of the quantifiers and replace the variables with two arbitrary constants just like the rule says:
$A(c)\to B(d)$
Okay now for the question... Let's also say that I have another premise, or perhaps just an assumption even, that says:
$A(d)$
Would it be usable with $A(c)$? Like, could I use the modus ponens rule like this:
$A(d)\quad A(c) \to B(d)$
The two constants $d$ and $c$ are different. I'mma guess the answer to this question is in fact "no" but it's something that keeps bothering me (because I always go like "Hmm but I can do this to appl--Oh... Guess not...)" and I just want to 100% make sure it's not possible since I am absolutely horrible at this subject!