Looking on the internet deeply has found these results:

but in fact is the most popular phrase on the web.

but in deed the results 10 results on the web	but in fact 11,220,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	Oct 13, 2013 ... She might come across as unfriendly, but in fact she is very kind and nice. ' Actually' and 'in fact' can be used to make things clearer or more�... But in fact the glorious beings which they had produced were tortured by subtle imperfections beyond their makers' comprehension. Paintings by Adolfo Bimer because everyday fears like not�... Well, it may sound very straightforward to you, but in fact it's all very complicated. Would you agree with me that teachers should refrain from socialising with their�... But, in fact, there is nothing that can bring you closer to fearlessness about everything else in the world than being a parent

but in deed the results

10 results on the web

but in fact

11,220,000 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

Oct 13, 2013 ... She might come across as unfriendly, but in fact she is very kind and nice. ' Actually' and 'in fact' can be used to make things clearer or more�...
But in fact the glorious beings which they had produced were tortured by subtle imperfections beyond their makers' comprehension. Paintings by Adolfo Bimer
because everyday fears
like not�...
Well, it may sound very straightforward to you, but in fact it's all very complicated. Would you agree with me that teachers should refrain from socialising with their�...
But, in fact, there is nothing that can bring you closer to fearlessness about everything else in the world than being a parent