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Combining plots


Hello all,


Suppose I wish to show a combined plot, for instance

a:=ListPlot[{1,2,3}]
b:=ListPlot[{4,5,5}]

using Show[a,b]

Now Mathematica draws 3 graphics, one of a, b and one of a and b 
combined. I want to only see the third combined graph and not the first 
two graphs. Is that possible?

I tried something with setting DisplayFunction to Identity in a and b, 
but then Show doesn't show anything... Help!

Thanks!

Johan


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