Subject to.....?

Hi! everyone.Could you tell me,whether my understanding about the sentence written below right?
I read in the warranty card of an electric appliance that-:The beneficiary customer entitled to this warranty subject to the terms and conditions stated below.-
Now my question is about the colored word (subject to),when I looked up in the dictionary,it said it means "likely to do or be" and in the second sense of its meaning I read "subject to" also meant "dependent upon" or "conditional upon",now I think in the sentence I wrote above,the second sense of "subject to" was used and if I rephrase the original sentence,will it be as-:The beneficiary customer's being entitled to this warranty is dependent upon the terms and conditions stated below-:.
If my sentence containing "dependent upon" is right? Can I use "conditional upon" by replacing "dependent upon"?
I will be very thankful if somebody tells me.
Thanks!