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The following are all equivalent to the original implication:

1. I am asleep if I dream.

2. I dream only if I am asleep.

3. In order to dream, I must be asleep.

4. To dream, it is necessary that I am asleep.

5. To be asleep, it is sufficient to dream.

6. I am not dreaming unless I am asleep.

The following are equivalent to the converse (if I am asleep, then I dream):

1. I dream if I am asleep.

2. I am asleep only if I dream.

3. It is necessary that I dream in order to be asleep.

4. It is sufficient that I be asleep in order to dream.

5. If I don't dream, then I'm not asleep.