Egg's Icemen all but out
Iceland now need to beat Denmark by three goals or more and hope the Swiss defeat Belarus to stand any chance of qualifying for the semi-finals.
Switzerland took the lead in the opening minute through Fabian Frei and increased their advantage just before half time with a goal from Innocent Emeghara. Jonsson played the full 90 minutes at right back.
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Hide AdIn the other match in Group A, goals from Christian Eriksen and Nicolai Jorgensen gave Denmark a 2-1 win over Belarus.
The result leaves both nations on three points in the group, with Switzerland on six and Iceland with no points.