Theorem bj-extru 31678

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 1842. (This is also extt 31408; propose to move to Main extt 31408 and allt 31405; relabel exiftru 1841 to exgen ? ). (Contributed by BJ, 12-May-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-extru	⊢ ∃𝑥⊤

Proof of Theorem bj-extru

Step	Hyp	Ref	Expression
1		tru 1478	. 2 ⊢ ⊤
2	1	exiftru 1841	1 ⊢ ∃𝑥⊤

Syntax hints:  ⊤wtru 1475  ∃wex 1694

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1700  ax-4 1713  ax-6 1838

This theorem depends on definitions:  df-bi 195  df-tru 1477  df-ex 1695

This theorem is referenced by: (None)