Theorem extru 1977

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 1978. (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 1546	. 2 ⊢ ⊤
2	1	exgen 1976	1 ⊢ ∃𝑥⊤

Syntax hints:  ⊤wtru 1543  ∃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 1969

This theorem depends on definitions:  df-bi 207  df-tru 1545  df-ex 1782

This theorem is referenced by:  euae  2661  nmotru  36621  wl-euae  37769