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This logic is not sound. Why couldn’t be the case that only one religion is right?
Three people looking at a triangle might have different opinions about what shape it is. It is inconceivable that they are all right, but that does not imply that they are all wrong.
I think the part that’s left out is “since they all can’t be right, yet use the same standard of authority for truth, the most likely scenario is that none of them have a reasonable claim to truth”.