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What is going on Under the hood in C# Compilation?

Simple and Very Intersting Problem:

From the below Code, I was wondering that In both conditions the Check variable will be true but i was wrong.

using System;
namespace Problem
{
    class Program
    {
        static void Main(string[] args)
        {
            int firstNumber = 1;
            int secondNumber = 9;

            bool Check = false;

            Console.WriteLine("Checking First Condition.");
            Console.WriteLine("------------------");
            if (firstNumber == (firstNumber = secondNumber))
            {
                Check = true;
                Console.WriteLine("First Check : {0}", Check);
            }
            else
            {
                Check = false;
                Console.WriteLine("First Check : {0}", Check);
            }

             Console.WriteLine("------------------");
             Console.WriteLine();
             Console.WriteLine("Checking Second Condition.");
             Console.WriteLine("------------------");

            // Resetting firstNumber value:
            firstNumber = 1;

            if ((firstNumber = secondNumber) == firstNumber)
            {
                Check = true;
                Console.WriteLine("Second Check : {0}", Check);
            }
            else
            {
                Check = false;
                Console.WriteLine("Second Check : {0}", Check);
            }
            Console.WriteLine("------------------");
        }
    }
}

But from while ago and thinking about it. but i can't get it why the first condition returning True

Dry Runs:

First Condition. (1 == (1 = 9) // firstnumber = 9. so 9 == 9 // True.

Second Condition. ((1 = 9) == 1) // firstnumber = 9. so 9 == 9 // True.

Output:

在此处输入图片说明

Can someone explain breifly what is happening under the hood ?

// What is done by a C# Compiler in both the cases ?.

conditions/expressions are evaluated from left to right. so,

 int firstNumber = 1;
 int secondNumber = 3;

First Case:

firstNumber == (firstNumber = secondNumber)
     1      == (firstNumber = secondNumber)
     1      == (     1      = secondNumber)
     1      == (     1      =      3      )
     1      ==   3
          false

Second Case:

((firstNumber = secondNumber) == firstNumber)

 (     1      = secondNumber) == firstNumber
 (     1      =      3      ) == firstNumber   
 (            3             ) == firstNumber   //firstNumber became 3
              3               ==     3 
                             true

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