Absent some other specific circumstance, a unit entering a province has no effect on a unit leaving that province.

I have an additional question about this, I knew support moves would be canceled out but what happens if I move into an area that another army is moving out of? I am hopping that the army would have to stay in this territory having to fight another army.

[quote=90kicvesb post_id=114457 time=1573971912 user_id=4813]
A unit cannot cut support for an attack on itself. Army C is dislodged.
[/quote]

Actually it can, if the attack succeeds in dislodging the supporting enemy unit.

[quote=90kicvesb post_id=114457 time=1573971912 user_id=4813]
A unit cannot cut support for an attack on itself. Army C is dislodged.
[/quote]

Further clarification for OP: army C is dislodged even if it attacked A with support from army D so long as A had enough support to hold.

A unit cannot cut support for an attack on itself. Army C is dislodged.

OK so what if Army A will support move Army B to Army C but Army C Will attack Army A. What the heck would happen here?