Artifact â Equipment
Equipped creature gets +4/+0.
At the beginning of your end step, if equipped creature didn't deal combat damage to a creature this turn, sacrifice it.
Bastien L. Deharme
Thirsting Axeâ€™s triggered ability checks whether the creature itâ€™s attached to at the moment your end step begins dealt combat damage to a creature earlier in the turn. It doesnâ€™t matter whether Thirsting Axe was attached to it (or to any creature at all) as combat damage was dealt.
If the equipped creature dealt combat damage only to a player or planeswalker, Thirsting Axeâ€™s triggered ability triggers. The same is true if the creature didnâ€™t deal combat damage at all.