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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.)
Ref Expression
extru 𝑥

Proof of Theorem extru
StepHypRef Expression
1 tru 1606 . 2
21exgen 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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