How to apply if-else condition of inputs and display the output on 7 segment display on Proteus
Here are some comments


First of all, note your circuit is fully digital. From the open-close switches to the 7 segment (or any other) display.
Lights (c.XIX) The simplest solution is to feed every door into a single LED. Easy. Good for most users. Probably the best solution, before the world ends. And clear to show which door is the one opened. And how many doors are opened. 
Gates (60') Lets assume you have just 4 doors. As you have realized, you can solve this purely with digital gates, such as the one you show. In this fashion this is a Standard Problem useful to exercise your skills (in this case, your proper domain of the Proteus simulator interface). All these are available in Proteus:


74HCT4002 Dual 4-input NOR Gate and 
74HCT02 Quad 2-Input NOR Gate for the NOR gates,
74HCT20 Dual 4-input NAND Gate and 
74HCT00 Quad 2-Input NAND Gate for the NOR gates, and
74HTC04 Hex Inverters, for converting the NOR and NAND in OR and NAND, if required, or 74HCT14 Hex Schmitt-Thriggered Inverters if in addition you need to compare small analog voltage levels.
74HCT126 Quadruple Bus Buffer Gate with Tristate Outputs, for some output control switching, and also for equalling the delay of an inverting gate, if required.

ICs (70') Now you have 7 doors, which means roughly 8 bits (obviously). This means nor 4 bit BCD, nor a 7 segment is enough for a 74HCT4511 BCD to 7 Segment Decoder. The easy way is to split the solution in 4 bit each, with two independent circuits. Now things are getting innecesarily cumbersome in the 70'. And also how to "encode" several doors opening at the same time. In here you are seriously thinking in going back in using simple LEDs (and you are right).
MCUs. You now figure it out. Finally, this is not the real way. If everything is digital, you should directly aim into a microprocessor (or something at the level), with 8 or more input and a way to integrate everything. There are really cheaper MCUs you can use which will discourage you to use any gate in the real life. But the gate way will give you an good skill on how to deal with digital concepts in a more analog fashion, how to work with delays, understand how the digital input output works, etc. Arduino or any similar platforms are the XXI century way to go.