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Here we have 59 in r1c27 and it's easy enough to see that r3c27 cannot BOTH be reduced to 59 only if we are to have a uniqe solution.
But how does the logic prove that NEITHER of r3c7 can be 9?

C4R9C8b6c7 digit 1 => r3c6 <>1

Pretty easy to spot one of many fish/coloring options .(not on my cpu to post the fish logic atm)

What you ask for is uniqueness assumptive logic of a unique rectangle probably type 4 if i recall correctly

edit: yup type 4

due to the strong link in row 3 for digit 5
see elevens notes below.

Thanx. It's true that fish can be found to solve this puzzle. For example the Skyscraper {1r29} => 9r7c9 stte.
I just thought it would have been easier to understand a more direct causal connection between the 59 Locked Pair and the elimination of the corresponding 9s in Row3

Withdrawn - eleven is right (as usual) .

Leren

Yogi wrote:Here we have 59 in r1c27 and it's easy enough to see that r3c27 cannot BOTH be reduced to 59 only if we are to have a uniqe solution.
But how does the logic prove that NEITHER of r3c7 can be 9?

It is called unique rectangle type 4.
You have a strong link for 5 between the UR cells in row 3, so one must be 5 and both must not be 9 to prevent the deadly pattern 5-9-5-9.

Gotcha. Thanx.