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The phrase "after reading through this" is correct and usable in written English.
It can be used to indicate that the speaker has completed reading a document or text and is about to provide feedback or a conclusion based on that reading.
Example: "After reading through this report, I believe we need to make some adjustments to our strategy."
Alternatives: "upon reviewing this" or "after going through this".
Similar(60)
Reading my mother's obituary, which he wrote, he stopped after reading through the list of his 12 surviving children and chuckled, "God, that's a lot of kids".
After reading through the Negotiation and Leadership brochure, my mind was made up: This was the program for me.
All participates in this project gave their written informed consent after reading through the consent forms.
After reading through the notes, the neurologist admonished me that nothing would be gained by pursuing this further if these spells happened so rarely.
After reading through the chapter, the reader should have a clear picture about popular global and detailed routing algorithms.
After reading through the front section, however, I found almost nothing on the race.
After reading through the Palm-PPP project, we realized that touch screen was not that hard to use.
The realtime clock and calender was very easy to setup after reading through the PIC32 documentation and examples online.
I watched it an hour or so after reading through the police report on Carlos's death.
After reading through the list of IEEE standards, we did not find much that we had to adhere to, due to the fact that our system is entirely self contained (i.e. does not use any RF devices, etc.).
After reading through the protest pages and information, I believe I came out with a better understanding of the NSA and will be more active in my opposition and awareness as well.
More suggestions(12)
after sifting through this
after living through this
after winding through this
after looking through this
after getting through this
after passing through this
after working through this
after going through this
after running through this
after suffering through this
after sitting through this
after walking through this
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com