Tricky predicate logic problem I'm having a hard time proving that this is a valid argument
$Premise 1: (Ǝx)Kx→(\forall x)(Lx→Mx)$
$Premise 2: Kc • Lc$
$Conclusion: Mc$
I am getting confused with all the existential/universal instantiation rules.
First I did:
$Kc\to\forall x(Lx\to Mx)$ by existential instantiation
then $Kc\to Lc\to Mc$ by universal instantiation
therefore $Mc$
Is there anywhere where I'm supposed to infer modus ponens since I've already been given Kc and Lc in premise 2??

Hint : assuming you are using Natural Deduction ...
From Premise-2 : $Kc \land Lc$ you have to derive $Kc$ (by $\land$-elimination), followed by $\exists x Kx$ (by $\exists$-introduction).
In this way, you can use $\to$-elimination (i.e. modus ponens) with Premise-1 and derive : $(∀x)(Lx \to Mx)$.
Now you have to use $\forall$-elimination (i.e. universal instantiation) with $c$ to get : $Lc \to Mc$.
