1. Induction to prove WFF

Let A and B be formula and p be a variable, prove with induction that A[p:=B] is a well-formed formula

i'm struggling with this question, i'm not sure about how to use the proper syntax in the proof I was hoping someone could point me in the right direction on where to start

2. Re: Induction to prove WFF

Since you are trying to prove that something is a "WFF", start with the definition of "well formed formula". What definition are you using?

3. Re: Induction to prove WFF

A word A is well-formed if and only if it is the last word of a formula calculation. Am I allowed to assume that A and B in the question are WFF themselves?

4. Re: Induction to prove WFF

If A is well-formed and I replaced every variable "p" in A with B, and B is well-formed, then it would make sense the new formula is well-formed but I have no idea how to write that out as an induction proof, i've only done those with numbers