Negative ない-Form VERB1 + で + VERB2 as “VERB2 without doing VERB1”
When expressing that the subject of the sentence performs a certain action (VERB2) without doing another action (VERB1) that is generally performed alongside it, then the grammar construct Negative ない-Form VERB1 + で + VERB2 can be used. In this form, both verbs must share the same subject. This construct also cannot be employed more than once in a single sentence because the ないで construction creates a subordination between the two clauses.
Te o arawanaide shokuji shita.
(I ate without washing my hands beforehand.)
Ha o migakanaide nemashita.
(I went to sleep without brushing my teeth.)
Kare wa shower o abinaide demashita.
(He left without taking a shower.)