what does "Synchronous exception from Current EL with SP_ELx" mean?

In here : https://chromium.googlesource.com/external/github.com/ARM-software/arm-trusted-firmware/+/v0.4-rc1/docs/firmware-design.md#bl1-architectural-initialization

The arm-tf B1 code sets the LED and SYS_LED[7:3] shows the exception class.

Some of them I show here. 

0x0 : Synchronous exception from Current EL with SP_EL0
0x1 : IRQ exception from Current EL with SP_EL0
0x2 : FIQ exception from Current EL with SP_EL0
0x3 : System Error exception from Current EL with SP_EL0
0x4 : Synchronous exception from Current EL with SP_ELx

I can't understand what "Synchronous exception from Current EL with SP_EL0" mean here. If a core is in ELx, isn't it using the SP_ELx?
When an exception is taken from a state, can the core have been in EL2 and and have been using SP_EL0 or SP_EL3?

p.s I don't know how to format the text style in this question window. (I wish there be format copy- format paste key here like in MS windows)