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
|- E. x T.

Proof

Step Hyp Ref Expression
1 tru
 |-  T.
2 1 exgen
 |-  E. x T.