I was wondering if someone can clear something up for me.
What exactly does it take for a given term or variable to be freely substitutable in a formula.
When would it be the case that...
1. (for every x(fi(x))---> fi(x))
2. (for every x(fi(x))---> fi(y))
3. (for every x(fi(x))---> fi(t))
where fi is a formula, x is a variable in fi, y is some variable, and t is some term
And those three sentences are to be considered separately.