How to prove the following claim using structural induction?

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The number of propositional variables is always at most one more than the number of connectives for every formula φ ∈ PROP.

where PROP is the set which represents all valid formula in propositional logic

I tried doing this proof in various ways, but I could not do it by structural induction.

Can someone explain how structural induction works and also how to prove the above claim using it.