Antibody Edicts work much the same way as the Antibody Challenge Cards. Each card has two values, and is marked with a color. The first value is what the edict normally is (Mobius Tubes, Forcefield, etc). The second value is always Cosmic Zap.
When a player of a color not listed on the card plays the edict, it can be used as the first value, OR they may play it as a Cosmic Zap on the color player listed on the card.

If a player of the color listed on the card has the Antibody Edict, they may only play it as a Cosmic Zap, and may play it on any other player.

Example: Blue holds an Antibody Edict with Red on the card. The card's values are Rebirth and Cosmic Zap. Blue may play the rebirth at any time, or he may play the Cosmic Zap on the Red player whenever appropriate.

Antibody Edict (Art by Jack Reda)
Conversely, if Red is holding the same card, he may only play it as a Cosmic Zap.

The benefit of the Antibody Edict card is being able to shuffle in some of the new or unusual Edicts, without reducing the chance of drawing a Cosmic Zap (arguably one of the most powerful and most important Edicts).

See also: Edicts

Expansion by Jack Reda