The phrase "a different proof of" is correct and usable in written English.
It can be used when referring to an alternative method or demonstration of a particular concept, theorem, or statement.
Example: "In this paper, we present a different proof of the Pythagorean theorem that utilizes geometric transformations."
Alternatives: "an alternative proof of" or "another proof of".
As a byproduct of our analysis we provide a different proof of an almost sharp local wellposedness in Hs(R+).
Also a different proof, of a deep result of J. Diestel, W. Ruess, W. Schachermayer about weak compactness in L1(E), is given.
My work with Murai and Stillman provides a different proof of the classical theorem that also proves the connectedness of the Hilbert scheme in new cases, including those of an exterior algebra and a Veronese ring.
For a different proof of (2.5), see [18] for details.
Remark 2.2 A different proof of (10) is given in [2].
Proof We want to present here a different proof of the lemma which uses the representations of extremal polynomials in (24).
In a different proof-of-concept clinical trial, autologous ADSCs were injected in patients with knee OA.
On the prooV platform, enterprises can test, evaluate and compare several technology solutions in the same proof-of-concept, rather than running a different proof-of-concept for each technology and having to compare the results afterward.
This is somewhat misleading, because, aside from implying an affinity to the Bitcoin blockchain (which uses a different, proof-of-work consensus algorithm), it also implies a considerable break with the past that hasn't really occurred, at least not on the technological level.
Then, we give a different proof for the existence and uniqueness of the solutions for linear coupled boundary value conditions for a differential system, i.e., Lemma 2.5.
In the paper, with help of variational principle and convexity analysis, we give the proof of existence in details and a different proof about the analytic expression of optimal solution.
