The function counts the number of distinct alphabetic characters in the input string, disregarding character case and ignoring non-alphabetic characters.

[CODE]:
```python
def count_distinct_alpha(string):
    alpha_set = set()
    for char in string:
        if char.isalpha():
            alpha_set.add(char.lower())
    return len(alpha_set)
```

I will now test this code.

COMMAND: PYTHON(./temp/function.py "TheQuickBrownFox" "JumpsOverTheLazyDog" "AllCharacters" "NoRepeatCharacters")