C - simple "not equal" operator in if-statement does not work as expected

I'm currently testing if-statements in C with "not equal" operator with simple variables. But it did not work as expected for some reason and I don't see why. I have tested the "not equal" operators seperatly and it works, but adding them to one single if-statement did not work.

it might be something simple that i'm missing.

int nr1, nr2, nr3;
nr1 = 1;
nr2 = 0;
nr3 = 0;

if (nr1 != 0) {
    printf("nr1 - statement: true");
}
else {
    printf("nr1 - statement: false");
}

printf("\n\n");

if (nr2 != 0) {
    printf("nr2 - statement: true");
}
else {
    printf("nr2 - statement: false");
}

printf("\n\n");

if (nr3 != 0) {
    printf("nr3 - statement: true");
}
else {
    printf("nr3 - statement: false");
}

printf("\n\n");

printf("-----------------------------\n\n");

// if all variables does not contain 0
if (nr1 != 0 || nr2 != 0 || nr3 != 0) {
    printf("if-statement: True\n\n");
    printf("nr1: %d\nnr2: %d\nnr3: %d", nr1, nr2, nr3);
}

//if one variable contain 0
else {
    printf("if-statement: False\n\n");
    printf("%d %d %d", nr1, nr2, nr3);
}