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The phrase "as it was shown" is correct and usable in written English.
You can use it when referring to something that has been previously demonstrated or illustrated in a discussion or text.
Example: "The results of the experiment were consistent with the theory, as it was shown in the previous section."
Alternatives: "as demonstrated" or "as illustrated".
Exact(60)
This protease was not substrate specific as it was shown to degrade leukotoxin.
CIAC presents interesting emergent properties as it was shown through some analytical test functions.
This effect is further pronounced with increasing precursor concentration as it was shown with experiments in a premixed flame reactor.
The magnetosheath ion flux turbulent flow is intermittent as it was shown earlier for the solar wind.
"They're engaging in jihad in a courtroom," said Debra Burlingame, who watched the arraignment as it was shown by live feed in a special facility in Brooklyn.
"California Dreamin' " is being released as it was shown in Cannes in 2007, which is to say in an unfinished (or, as the title parenthetically suggests, "endless") state.
A frame from a video as it was shown last week on ABC News shows an Afghan grain merchant being tortured in Abu Dhabi.
Notably, photopatterned VEGF retained native functionality as it was shown to induce morphological changes in human umbilical vein cells indicative of early vasculogenesis.
It is worthnoting that in case of disturbances, pinches behave in very complex manner as it was shown in [1 5].
A spore forming bacteria Bacillus licheniformis 421 was used as it was shown to be a good candidate in a previous study.
However, when deposited on polyamide or polyester fabrics, this coating displays different morphologies as it was shown by scanning electron microscopy (SEM) analysis.
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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