equilateral tringles

Let ABC be an equilateral triangle. Points A_1,B_1,C_1 are chosen inside the triangle in such a way that A_1 \in CC_1, B_1 \in AA_1, C_1 \in BB_1 and AB_1=B_1A_1, BC_1=C_1B_1, CA_1=C_1A_1. Prove that the triangle A_1B_1C_1 is also equilateral.

I'd be very grateful if someone could help me.
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