Antifoams (usually consisting of a mixture of hydrophobic solid particles and oils) are widely used in different technological applications to prevent the formation of excessive foam. Uncertainty still exists in the literature about the actual mechanisms by which these substances destroy the foam. To elucidate this problem, we have performed microscopic observations on the process of foam film destruction by means of a high-speed camera. Horizontal and vertical foam films (obtained from solutions of the surfactant sodium dioctyl sulfosuccinate) were studied in the presence of antifoam particles containing silicone oil and hydrophobized silica. The observations show that in this system the antifoam particles destroy the foam lamella by the formation of unstable oil bridges, which afterward stretch and eventually rupture, due to uncompensated capillary pressures across the different interfaces. These bridges can be formed either from initially emulsified antifoam droplets, which enter both surfaces of the foam film during its formation and thinning, or from oil lenses which float on the bulk air-water interface even before the foam film is formed. We show that the presence of an oil layer having a thickness of several nanometers, prespread over the foam film surfaces, is very important for the process of lamella destruction, because this layer substantially facilitates the entry of the oil drops on the film surface and the formation of unstable bridges. The process of oil-bridge stretching, which is usually not considered in the standard mechanisms of antifoam action, is theoretically analyzed in the second part of this study.