If it hadn't been for B777, T800 would have been cancelled, the SIA order saved it.
Also, BA, traditionally a RR customer specified GE90 for it's initial B777 order. This was unashamedly done as part of a deal whereby GE bought BA Engine Overhal Limited (BAEOL) in South Wales, this deal also saved the GE90 from extinction at that time.
Off topic - Sorry