I want to show that
$$ (\lambda fgx. fx(gx)) (\lambda xy. x) (\lambda xy.x) = \lambda x. x $$
Here's my try:
$$ (\lambda fgx. fx(gx)) (\lambda xy. x) (\lambda xy.x) = (\lambda fgx. fx(gx)) \underline{true} \ \underline{true} = \lambda x. \underline{true} \ x (\underline{true} \ x) = \lambda x. (\underline{true} \rightarrow x \ | \ \underline{true} \ x) = \lambda x. x $$
$\square$
Are the steps correct and reasonable? Thanks a bunch!