Abbreviate Conditional Proof to CP, Statement Function to SF, and Universal Quantifier to UQ.
Source: p 483, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley
The next example differs from the previous one in that the antecedent of the conclusion is a statement function, not a complete statement. With arguments such as this, only the statement function is assumed as the first line in the conditional sequence. The quantifier is added after the sequence is discharged.
Earlier, p 464 stated the necessity of removing all quantifiers before applying any Rule of Inference. So how is the bold correct? Why can you correctly assume only the SF?