Does <execution have priority over ==?

For the following code:

int main()
{
    int a, b, c, d;
    c = 5;
    d = 5;
    a = 10;
    b = 8;
    if (a == c++ && b < d++);
    printf("c=%d d=%d\n", c, d);
    return 0;
}

Output: c=6 d=5

I know, since the first expression in the if expression takes the value false, the second expression is not evaluated and therefore is output. However, I read the following words in ANSI C from Balaguruswamy:

Since the operator <has a higher priority than ==, b < d++first evaluated, and then a == c++.

Now, according to this, the value dshould not be 6, but not c?