standard error for difference in prediction using R

Question

I want to calculate standard error for difference between two predictions, but have little idea.

Please see the code below:

pred <- predict(hsg_prob, newdata=data.frame("three_kids" = 1,
                                               "post_arra" = c(0,1),
                                               "three_x_arra" = c(0,1)),
                   se.fit = TRUE,
                   type = "response")

pred

This gives me

$fit
        1         2 
0.7469388 0.7578797 

$se.fit
         1          2 
0.01388808 0.01621392 

$residual.scale
[1] 1

What I am interested in is the standard error of pred$fit[2]-pred$fit[1], which is the standard error of these two predictions 0.7578797 - 0.7469388

I also tried using diff(pred), but it doesn't come out with a standard error.

Is there any easy way to calculate standard error for this?

Thanks!