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Theorem bj-extru 32779
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 1949. (This is also extt 32528; propose to move to Main extt 32528 and allt 32525; relabel exiftru 1948 to "exgen", for "existential generalization", which is the standard name for that rule of inference ? ). (Contributed by BJ, 12-May-2019.) (Proof modification is discouraged.)
Ref Expression
bj-extru 𝑥

Proof of Theorem bj-extru
StepHypRef Expression
1 tru 1527 . 2
21exiftru 1948 1 𝑥
Colors of variables: wff setvar class
Syntax hints:  wtru 1524  wex 1744
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-6 1945
This theorem depends on definitions:  df-bi 197  df-tru 1526  df-ex 1745
This theorem is referenced by: (None)
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