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Theorem extru 1981
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 1982. (Contributed by Anthony Hart, 13-Sep-2011.) (Proof shortened by BJ, 12-May-2019.)
Assertion
Ref Expression
extru 𝑥

Proof of Theorem extru
StepHypRef Expression
1 tru 1542 . 2
21exgen 1979 1 𝑥
Colors of variables: wff setvar class
Syntax hints:  wtru 1539  wex 1781
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-6 1971
This theorem depends on definitions:  df-bi 210  df-tru 1541  df-ex 1782
This theorem is referenced by:  euae  2748  nmotru  33813  wl-euae  34867
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