Hi everyone.

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.