私まで嬉しい is translated as "I am happy", what function of まで is this?


Why is it used this way instead of は for example?




The まで means "even".

According to 明鏡国語辞典:

> まで ㊁〘副助詞〙  
>  ❶ 極端なものを例示して、他はましてと暗示する。「君 **まで** 僕を疑うのか」「親に **まで** 見限られるとは」

It is used to show an extreme example, implying that some other thing(s)
is/are much more so.

> 私 **まで** 嬉しい。  
>  " _Even_ I am happy (as well as someone. / and others are much more so)."  
>  (It's closer to 私 **も** 嬉しい "I'm happy, too" than 私 **は** 嬉しい "I'm happy.")

An example from Shogakukan's Progressive Japanese-English Dictionary:

> 老人 **まで** 踊っている。 **Even** old people are dancing.

