Then I'm going to give you a chance to prove your loyalty.
I came to you in order to prove my loyalty.
"We do it just to prove our loyalty to the president."
She is out to prove her loyalty to the humans.
But those forces have yet to prove their loyalty or effectiveness.
"One day you will prove your loyalty to me, do not doubt."
"You do not need to exhaust yourself in my service to prove your loyalty."
What more could she have done to prove her loyalty to Archer?
"You proved your loyalty beyond any reasonable doubt a couple of days ago."
In the case of the guards, it also proved their loyalty.