Theorem nexntru 33747

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

Assertion

Ref	Expression
nexntru	⊢ ¬ ∃𝑥 ¬ ⊤

Proof of Theorem nexntru

Step	Hyp	Ref	Expression
1		tru 1537	. . 3 ⊢ ⊤
2	1	notnoti 145	. 2 ⊢ ¬ ¬ ⊤
3	2	nex 1797	1 ⊢ ¬ ∃𝑥 ¬ ⊤

Syntax hints:  ¬ wn 3  ⊤wtru 1534  ∃wex 1776

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792

This theorem depends on definitions:  df-bi 209  df-tru 1536  df-ex 1777

This theorem is referenced by:  neutru  33750