Armstrong is correct, but let me explain what happens here:
the condition field is, if you didn't know, all the things that NEED to happen before the things in the on Activation field CAN happen. Alright, so, you put !(alive bmp1) in the condition field of one trigger. This trigger will shoot once bmp1 is destroyed, although with vehicles I'd almost suggest the !(canMove bmp1) or !(canFire bmp1), since they can often get disabled without actually being "destroyed" as per OFP's requirements. The ! by the way is just another way of saying not, so !(alive bmp1) means not(alive bmp1). And yes, you can use NOT too.
*ahem*
Now, the second part. The variable armstrong uses there is a fine tool and the most common one too. By putting for instance: bmpDestroyed=true in the on activation field makes the variable bmpDestroyed true. And by then creating another trigger with the condition, as armstrong says, bmpDestroyed, will activate that trigger as soon as the bmp is killed.
Better hurry this up now. Ehm, you want to create an extraction zone? Maybe a small area, say 100 x 100? Well, create your trigger, make it activated by: West (or east or resistance or whatever you are). Then, in the condition field write: this AND bmpDestroyed
why? Well, if you walk into the radius without the variable being true, nothing happens, since you need not only the presence of west ("this", referring to the Activated By function) but ALSO that the bmp is destroyed. You rarely need to define variables beforehand, and all which are mentioned somewhere (but not yet defined, as per variableName=true or variableName=false somewhere yet) are considered false.
And then...well, make it type End #1 if you want the mission to end, otherwise do whatever you want with the on Activation field.
Argh, sorry it's late and I'm might blather a bit. Hopefully you've got some help outta this, and if there's something that needs clarification (which I'm sure there is... :-\ ) just ask away.
;D Wolfrug out. ;D