Conditional independence

Dear all,

I have a question that seems difficult for me to figure out. I hope you would help.

Suppose we have following random variables:

Y1 = X + N1;
Y2 = X + N2;
where X, N1, and N2 are independent of each other.

Can I write: p(Y1Y2|X) = p(Y1|X)*p(Y2|X) ???

Thanks for reading and hope to hear your answer.

Best regards,
nhamhiemlam