No, that's not how an expense works. Startup costs less than $5,000 are a miscellaneous expense and like your other business expenses, reduces your net profit or increases a loss. Net profit/loss is then added/subtracted from your other income items and the total (less standard/itemized deduction) is what you pay income taxes on.
Net profit is also subject to self-employment taxes, though you do get a deduction for 1/2 of the amount. Expenses are not a dollar for dollar reduction in tax liability.
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