Preprocessor and double declaration include in different files

I am wondering how compiler (or preprocessor) include headers. I have three files. First is header.h, second first.cpp <- and there is #include <iostream>, third <- it contains #include <iostream> too.

header.h:

#ifndef HEADER_H_
#define HEADER_H_

struct Student
{
    std::string imie;
    int ocena;
};


void foo();

#endif

first.cpp:

#include <iostream>
#include "header.h"

int main()
{
    Student Jan;
    std::cout << "It's OK" << std::endl;
    foo();

    return 0;
}

Second.cpp:

#include <iostream>
#include "header.h"

void foo()
{
    std::cout << "I like Linux" << std::endl;
}

And my question is do the compiler copy code from library twice? Should I cut all iostream from .cpp's to one .h?