Theorem nextnt 32404

Description: There does not exist a set, such that ⊤ is not true. (Contributed by Anthony Hart, 13-Sep-2011.)

Assertion

Ref	Expression
nextnt	⊢ ¬ ∃𝑥 ¬ ⊤

Proof of Theorem nextnt

Step	Hyp	Ref	Expression
1		tru 1487	. . 3 ⊢ ⊤
2	1	notnoti 137	. 2 ⊢ ¬ ¬ ⊤
3	2	nex 1731	1 ⊢ ¬ ∃𝑥 ¬ ⊤

Syntax hints:  ¬ wn 3  ⊤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

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

This theorem is referenced by:  unnt  32407