In diode D₃ Case

The applied voltage at cathode terminal of the diode D₃ is +1V & applied voltage at the anode terminal of the diode D₃ is +5V therefore the potential difference is 4V. that's mean the anode  terminal of the diode D₃ is more positive as compare  to the cathode terminal of the diode the D₃ so it shall be in forward biased condition that is  D₃ is ON.

D₁ & D₂ are off.

In diode D₂ & D₁ case:

The potential difference across the diode D₂  is 3 V. that's mean the anode terminal of the diode D₂ is more positive in comparison of the cathode terminal of the diode D₂ but potential difference is less than like in case of diode D₃ , therefore diode D₂ is in forward biased condition however this is not as much forward -biased like in the case of the diode D₃  due to this we are letting the case of ideal diodes we let that the while diode D₃ is fully forward biased and this shall pass more current than diode D₂ & D₁.         

Because of the forward biasing of diode D₃ this potential difference shall supply on output & this potential difference operate the diode D₂ & D₁ in reverse biased

D₁ & D₂ are off.

D₃ is ON

                                                So V=+1V

                                                Also by using Ohm's Law

                                                                I = (5-1)/1k=4mA