If you precompose the symbols, you can use Linear Wipe.
If you actually want them to dissolve up individually, Here's one way to do it:
Add your symbols to the comp & position them.
Animate the Opacity property from 0 to 100 on the FIRST symbol.
Highlight both keyframes and copy.
Select the remaining layers and paste; now all layers' opacity property is animated.
Select all layers and use the Sequence Layers command, which will move the in point of each the desired distance down the timeline from the in point of the previous layer.
