extru - Metamath Proof Explorer

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Theorem extru 2025

Description: There exists a variable such that ⊤ 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 2026. (Contributed by Anthony Hart, 13-Sep-2011.) (Proof shortened by BJ, 12-May-2019.)

**Assertion**
Ref	Expression
extru	⊢ ∃𝑥⊤

**Proof of Theorem extru**
Step	Hyp	Ref	Expression
1		tru 1606	. 2 ⊢ ⊤
2	1	exgen 2024	1 ⊢ ∃𝑥⊤

Colors of variables: wff setvar class

Syntax hints: ⊤wtru 1602 ∃wex 1823

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-6 2021

This theorem depends on definitions: df-bi 199 df-tru 1605 df-ex 1824

This theorem is referenced by: euae 2690 nmotru 32991 wl-euae 33895

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