English forgotten by the American, just like that (4)
I believe the answer is:
thus
'just like that' is the definition.
(thesaurus)
'english forgotten by the american' is the wordplay.
'english' becomes 'e' (abbreviation).
'forgotten by' is a deletion indicator.
'american' becomes 'us'.
'the' with 'e' taken out is 'th'.
'th'+'us'='THUS'
(Other definitions for thus that I've seen before include "Consequently" , "In this way" , "It follows" , "'So, therefore (4)'" , "as indicated" .)