I have some troubles proving soundness for $\forall$ Introduction. Let $T_1,...,T_n\vdash Q$. $\forall$ Intro gives that $T_1,...,T_n\vdash \forall x Q[x/t]$. Here, t is a constant symbol that does not occur in ${T_1,...,T_n}$, x is a variable which does not occur in Q.
I understand it intuitively, but have some problems with tarskis' truth definitions. Thank you for your answer.