Vegans would die!

Without photosynthesis there would be no supply of oxygen and slowly the oxygen would get used up by oxidation such as rust formation. Furthermore, by removing plants, all of the many many animals that depend on plants would get very very hungry and gradually die.

The food chain of almost all animals rely on photosynthesis. We eat plants (which photosynthesize) and animals. Animals eat other animals (which eat plants) and plants. Plants photosynthesize. So, large animals (like us) in general probably wouldn't exist. There are a couple ecosystems that don't use photosynthesis to supply all their energy. These get their energy from heat-loving bacteria that live on underwater volcanoes and get their energy there. These ecosystems are very deep in the ocean and include worms and blind crabs. They're pretty creepy, here are a lot of the crabs living on a volcanic vent near antarctica:

It can be difficult to know what would happen if you made such a dramatic change to the world. But one thing we know for sure is that animals wouldn’t exist and any living things left would be microscopic. Many living things obtain their energy directly from the sun in the case of plants or indirectly as in the case of animals. If there was no photosynthesis, plants and animals likely could not exist. In addition the atmosphere would have very little oxygen because photosynthesis releases a large amount of oxygen into the air. It is possible that some very basic organisms could still exist like the deep sea vent bacteria that don’t get their energy from the sun. In fact, some scientists think that the first cells ate chemicals that were created in the atmosphere. So cells like these might continue to live. Otherwise, the Earth would be a pretty barren lifeless place without photosynthesis.

If there was nothing on Earth that could do photosynthesis, then the only life on Earth would be small bacteria and other things similar to bacteria. Most life on Earth depends on photosynthesis. Plants use photosynthesis to make sugar for energy and most animals need plants for food. Even carnivores, like lions, need plants, because their prey (animals like antelope) eat them.

The Earth would still have an iron-rich ocean. I don't know whether the air would have more carbon dioxide, or if all of the carbon dioxide would have been locked away in carbonate rocks and we would have an entirely nitrogen atmosphere. Life would be found only in geothermal vents where it is possible to get energy without relying on the sun. There would be no "advanced" multicellular life such as the kinds that we are familiar with.