Income Tax computation

In Chapter 2,example 8 (Kai), the lecturer reduces the Gross income by the amount of the (tax deductible) personal pension contribution, to give the Adjusted Net Income. This gives the personal allowance. To determine the taxable income, the lecturer then reverts to the gross income, not the Adjusted taxable income. Kai thereby loses the tax reduction arising from investing in a personal pension contribution. Surely this cannot be right?