By the standard interpretation of the representing logical formula,
(1)
If is first-order consistent, part (b) supplies the right-hand side, so is true. If is inconsistent, explosion gives , so the representing existential statement is true and is false. Therefore
(2)
This is an external truth assertion about the standard natural numbers. Formalizing that assertion inside a first-order theory requires the additional facts explicitly supplied in part (d).

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