Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9×13-inch pan.

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In a large bowl, combine the flour, sugar, cocoa, baking soda, baking powder and salt. Make a well in the center and pour in the eggs, coffee, milk, oil and vinegar. Mix until smooth; the batter will be thin. Pour the batter into the prepared pan.

Bake in the preheated oven for 35 to 40 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow to cool.