No, it's a second-order statement, a statement about first-order statements. It's not subject to itself.
If it's not subject to itself, then it's claiming an exception to its own rule, which makes it self-defeating. A universal claim about truth can't exempt itself without contradiction.
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If it's not subject to itself, then it's claiming an exception to its own rule, which makes it self-defeating. A universal claim about truth can't exempt itself without contradiction.