Not that

In spoken English especially, not that can be used when one assertion contrasts with another logically. It's like saying  "that doesn't mean that".

E.g.

Lunch is incomplete without the daily news. Not that anyone actually listens to it, mind you — La comida no está completa sin el telediario. Eso sí, no es que le hagan mucho caso.

The problem of dog shit on the street is getting worse- not that anyone cares, of course — El problema de la mierda de perro en las calles va a peor - aunque no es que le importe a nadie, claro

See more examples