The basic answer is `probably yes', that if Condition A has significantly > 0 and Condition B is non significantly < 0, then Condition A is significantly > B, but there are a couple of ways to be sure...

Firstly, when fitting a linear or generalised linear model, an 'identifiability constraint' is used. One common one is 'sum-to-zero' where the parameter estimates for all the groups will sum to 0, and another is to set one of the groups to 0, so that all the others will be in comparison to that.

I guess the program you are using does the latter, with the control group set to 0? If so, then you could change it so that group A or B is set to 0, and then you can see if the other is significantly different. This would be a statistically sound way of testing group A and B.

A second way would be using confidence intervals. If you haven't come across these before

http://en.wikipedia.org/wiki/Confidence_interval seems to cover it fairly well. Basically, if you want to test whether A=B at the 5% significance level, you look at the 95% confidence intervals for A and B, and see if they overlap. If they do, then you do not reject A=B at the 5% level, and if not, then you do reject.