Theorem bj-extru 32654

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 1892. (This is also extt 32403; propose to move to Main extt 32403 and allt 32400; relabel exiftru 1891 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.)

Assertion

Ref	Expression
bj-extru	⊢ ∃𝑥⊤

Proof of Theorem bj-extru

Step	Hyp	Ref	Expression
1		tru 1487	. 2 ⊢ ⊤
2	1	exiftru 1891	1 ⊢ ∃𝑥⊤

Syntax hints:  ⊤wtru 1484  ∃wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-6 1888

This theorem depends on definitions:  df-bi 197  df-tru 1486  df-ex 1705

This theorem is referenced by: (None)