A friend of mine said: "The reason slippery slope arguments are falatious is because we always make each step in a reasoned way, and they assume that everything will be automatic after the first step."

Your friend correctly described a fallacious use of the slippery slope. However, you incorrectly applied it to an argument in which the slippery slope is not used fallaciously.

The slippery slope argument is fallacious when, as your friend described, it assumes that a number of steps in between must occur before reaching the bottom of the slope.

In this case, no steps at all are being assumed. If A is true due to arguments 1, 2, 3, 4, and 5 and those same arguments apply to B, then B must also be true unless there are other arguments unique to B which render it untrue. This is logically sound. It is not a fallacious use of the slippery slope.

Like the appeal to authority and other popular fallacies, the slippery slope has fallacious and non-fallacious implementations. This one was logically sound. No steps are required to get from A to B.