The discovery was made around 8:25 a.m. Saturday in the 5300 block of Chestnut Street.
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That's where officers found the victim, a woman in her early 30s, in the passenger seat of a gold Honda Odyssey.
The victim had multiple stab wounds to her body and one in the face, police say.
She was pronounced dead at the scene.
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Philadelphia police said Saturday night that person of interest was in custody. He was only identified as a 34-year-old man.
The name of the victim has not been released.