Is it always true to presume that the logical and operator won't evaluate the second expression if the first one is false?

Question

int* ptr;
//ptr may points to any location(e.g. nullptr)
if(ptr != nullptr && *ptr != 1) {
  //A
} else {
  //B
}

so are the above codes always equivalent to the following ones?

if(ptr != nullptr) {
  if(*ptr != 1) {
    //A
  } else {
    //B
  }
} else {
  //B
}

I wonder if this rule a standard or implementation-defined, and is the first piece of code portable?