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s f g x = f x (g x)

k x y = x

b f g x = f (g x)

c f g x = f x g

y f = f (y f)

cond p f g x = if p x then f x else g x

fac = y (b (cond ((==) 0) (k 1)) (b (s (*)) (c b pred)))

You don't need if-then-else, you can emulate it by applying k and (s k) (which can represent true and false).