[HayZee518]

In this case, then, however your installation is illegal. to feed a sub panel you must use a four wire cable known as SER . Essentially it is a three wire cable with a wrapped ground - a white colored cable, a black one, a red one and the bare wrapped stands that make up the ground, plus a thermoplastic cover. if you are using seperate wires of no 6 in conduit you must run another bare ground from the main panelbox along with them in the same conduit to your sub panel. at the sub panel you isolate the neutral bus (i.e. no bonding screw) and a seperate grounding bar that the bare ground would go to. at the main panel both the bare ground and the white colored wire would go to ITS neutral bus bar. [this bus bar IS bonded to case ground.] Although your thought process seemed ok to make a splice in the feeder it does not meet code standards for a remote panel installation. don't rely on me alone, but if you run another bare ground to the sub it may qualify for a four wire to the sub. check with speedy pete before you complete this.