It sounds like you need an OR instead:

<button type="submit" [disabled]="!validate || !SAForm.valid">Add</button>

This will disable the button if not validate or if not SAForm.valid.

In addition to the other answer, I would like to point out that this reasoning is also known as the De Morgan's law. It's actually more about mathematics than programming, but it is so fundamental that every programmer should know about it.

Your problem started like this:

enabled  = A and B
disabled = not ( A and B )

So far so good, but you went one step further and tried to remove the braces. And that's a little tricky, because you have to replace the and/&& with an or/||.

not ( A and B ) = not(A) OR not(B)

Or in a more mathematical notation:

I always keep this law in mind whenever I simplify conditions or work with probabilities.

Declare a variable in component.ts and initialize it to some value

 buttonDisabled: boolean;

  ngOnInit() {
    this.buttonDisabled = false;
  }

Now in .html or in the template, you can put following code:

<button disabled="{{buttonDisabled}}"> Click Me </button>

Now you can enable/disable button by changing value of buttonDisabled variable.