Theorem nextnt 31574

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 1479	. . 3 ⊢ ⊤
2	1	notnoti 136	. 2 ⊢ ¬ ¬ ⊤
3	2	nex 1722	1 ⊢ ¬ ∃𝑥 ¬ ⊤

Syntax hints:  ¬ wn 3  ⊤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

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

This theorem is referenced by:  unnt  31577