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The slippery slope fallacy is committed only when we accept without further justification or argument that once the first step is taken, the others are going to follow, or that whatever would justify the first step would in fact justify the rest. Note, also, that what some see as the undesirable consequence lurking at the bottom of the slope others may regard as very desirable indeed.
Howard Kahane and Nancy Cavender, Logic and Contemporary Rhetoric, 8th ed., Wadsworth, 1998
Slippery slope. I carry a spare shirt; pretty soon I'm carrying spare pants. Then I'd need a suitcase. Next thing I know, I've got a house and a car and a savings plan and I'm filling out all kinds of forms.
Lee Child
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-Nik