The closer the garment to your body, the stronger is the Chiyuv of Keri’ah. i.e. The shirt is much stronger obligated in Keri’ah than is a jacket. This absolutely is also Halocho for Ashkenazim. Lamentably, I have seen many Availim with torn jacket but intact shirt, but it is not my job at a Shiva to grieve an Oveil, so I refrain from saying anything and hope their local Rov will correct them.
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