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Metamath Proof Explorer

Theorem extru

Description: There exists a variable such that T. holds; that is, there exists a variable. This corresponds under the standard translation to one of the formulations of the modal axiom (D), the other being 19.2 . (Contributed by Anthony Hart, 13-Sep-2011) (Proof shortened by BJ, 12-May-2019)

		Ref	Expression
	Assertion	extru	⊢ ∃ 𝑥 ⊤

Proof

Step	Hyp	Ref	Expression
1		tru	⊢ ⊤
2	1	exgen	⊢ ∃ 𝑥 ⊤