Complex sentence: In the case of the existential quantifier, I found Gödel's inductive proof somewhat hard to explain because he introduces a non-subscripted variable in the formula for the inductive hypothesis, while the class existence theorem is stated for subscripted variables.
Split into simpler sentences: In the case of the existential quantifier, I found Gödel's inductive proof somewhat hard to explain because he introduces a non-subscripted variable in the formula for the inductive hypothesis. However, this formula does not have the form expected by the induction hypothesis since the class existence theorem is stated for subscripted variables.