It's probably always important to add the little note about "
equivalent framing". If you shoot at a
constant distance, a 50/1.8 on a crop has the same real DoF as a 50/1.8 on a full-frame. But if you shoot the
same framing between crop and FF, then yes, the FF has less DoF because you're actually physically closer to the subject... meaning a closer focusing distance, and therefore a more-shallow DoF. If you wanted the same apparent DoF with identical framing (i.e. filling the frame on both crop and FF), then you have to stop down the lens on FF by the crop factor to achieve the same "look".
It's confusing if you let it be

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Canon EOS 5D MkII | Canon EOS 7D | Canon Digital Rebel XSi | EF 35mm f/1.4L | EF 50mm f/1.8 II | EF 85mm f/1.8 | EF 100mm f/2.8 Macro USM | EF 135mm f/2L | EF-S 18-55mm f/3.5-5.6 IS | 580EX II | LumoPro LP-120
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