Theorem extt 31573

Description: There exists a set that holds ⊤ as true. (Contributed by Anthony Hart, 13-Sep-2011.)

Assertion

Ref	Expression
extt	⊢ ∃𝑥⊤

Proof of Theorem extt

Step	Hyp	Ref	Expression
1		allt 31570	. 2 ⊢ ∀𝑥⊤
2		19.2 1879	. 2 ⊢ (∀𝑥⊤ → ∃𝑥⊤)
3	1, 2	ax-mp 5	1 ⊢ ∃𝑥⊤

Syntax hints:  ∀wal 1473  ⊤wtru 1476  ∃wex 1695

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-6 1875

This theorem depends on definitions:  df-bi 196  df-tru 1478  df-ex 1696

This theorem is referenced by:  mont  31578