Hi:
Yes, "no hay de que" is basically "de nada".

I agree with Idalmis, but if you really want to make a distinction, it might be like this.

No hay de que = Don't mention it
De nada = You're welcome

BTW, it's never "da nada," as in your title.

No hay de que, which is what I almost always use, don't know whether it is an old saying, don't mention it. Viva Linguaphone.

Thank you James for clearing this up.

I am trying to be careful with my spelling, but in a complicated long sentence like 'de nada' one can make a little mistake.

There is no spell checker here for Spanish, is there'

I don't know, but spell checkers don't work as well with languages that have lots of conjugations (especially Russian). "Da" is a correctly spelled word in Spanish ("gives"), so a checker wouldn't catch it anyway.

Thank you Eddy.
I figured (based on nothing) that de nada would be the norm. That is why I am only on Spanish 100.25 level. Again

I was just looking at my native vowels (14), and a total of 44 'letters' (sounds') all based solely on Latin characters. There is no way can one make a spell checker for some languages. A grammar checker may be easier (like the one WordPerfect had for English).