We report highly sensitive de Haas-van Alphen (dHvA) effect measurements on a high-mobility two-dimensional electron system in an AlAs quantum well. Here two valleys are occupied forming a pseudospin system. At 400 mK, the dHvA effect shows pronounced oscillations at filling factors nu=1 to four. In the quantum limit at nu=1 the data are consistent with an interaction-enhanced valley splitting, which exceeds the Zeeman spin splitting in a perpendicular field B. When tilting B the energy gap Delta E at nu=1 shows first an unexpectedly strong angular dependence and then remains constant. This suggests a crossover in the energy gap, most likely from a spin to a pseudospin gap. We attribute the strong initial dependence of Delta E on the tilt angle to skyrmion-type spin excitations. Surprisingly, the dHvA oscillation amplitudes do not display coincidence phenomena at higher filling factors. This is explained by the large valley splitting and avoided crossings of energy levels.