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I'm asking about "W" and not "X" here.

Claim 1: A system comprising X, Y, Z.

Claim 2: The system of claim 1, wherein the X is connected to a W.

Claim 3: The system of claim 1, wherein the W is P connected to U.

In claim 3, I introduced "w" with the definite article. Even though the parent claim (claim 1) does not mention "w", a sister claim (claim 2) already mentioned "w" so antecedent basis is already established. Is it correct?

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Yes to the body of the question, No to the title of the question

You can imagine a dependent claim as being re-written as concatenated at the end of the independent claim. If there is "an X" in the independent claim the dependent claim should use "the X". If the dependent claim has "an X", it could be ambiguously seen as introducing a second X.

Since claim 3 depends on claim 1, it does need to introduce W as "a W". The fact that claim 2 introduces W is irrelevant to claim 3 even though 2 comes before 3.

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    Yes, and in this case claim 3 depends upon claim 1, which does not introduce W, so claim 3 cannot refer to "the W", it should be "a W". The "a W" of claim 2 is irrelevant as long as the subsequent claim does not depend upon claim 2. Sep 18, 2019 at 5:58

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