but as we have shown above vs but as shown above

Both phrases are correct, but "but as shown above" is more concise and commonly used. The phrase "but as we have shown above" is also correct but may sound slightly redundant.

Last updated: March 19, 2024 • 1021 views

but as we have shown above

This phrase is correct but may sound slightly redundant.

This phrase is used to refer back to something that has been demonstrated or explained earlier in the text.

Show examples from the web [+]

But as we have shown above, it is possible to draw very different conclusions about product safety depending on whether specific or overall safety is the ...
Jun 17, 2014 ... But, as we have shown above, only the richest households in the economy owned bonds. The collapse in house prices hit low-net-worth ...
But as we have shown above, such designs cannot be constructed, anyway. If n is a prime, then Hedayat and Federer [3] have given a simple algorithm.
Nov 24, 2013 ... The integration over A is in principle of the area of the entire source, but as we have shown above this is limited to a region of width vtcool or ...

Alternatives:

but as shown above
as demonstrated above
as illustrated above
as previously shown
as indicated earlier

but as shown above

This phrase is concise and commonly used.

This phrase is used to refer back to something that has been demonstrated or explained earlier in the text.

Show examples from the web [+]

Incremental binding energies confirm {28, 50, 82, 126}. but, as shown above, reveal 6 and 14 as filled shell magic numbers. There is a degree of magicalness to ...
The change in potential energy involved in a pair formation would seem to be independent of all conditions of the nucleons, but as shown above for the case of ...
The default Theme is Signal but, as shown above, you can use other themes. More information about themes can be found in our document Working with ...
CleverCSS does not process selectors in a special way, but as shown above you can nest selector blocks instead of repeating parent selectors in individual ...

Alternatives:

but as we have shown above
as demonstrated above
as illustrated above
as previously shown
as indicated earlier

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but as we have shown above vs but as shown above