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Smashing with a cw-complex preserves weak equivalences between well-pointed spaces

By well-pointed i mean that the inclusion of the base point is a h-cofibration, weak equivalences are the usual weak homotopy equivalences between spaces. this is claimed as part of theorem 6.9 (i) in model categories of diagram spectra but as far as i can see without reference. can anyone point me to some place in the literature or indicate where this statement comes from ?