Theorem nexntru 36948

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 1574	. . 3 ⊢ ⊤
2	1	notnoti 144	. 2 ⊢ ¬ ¬ ⊤
3	2	nex 1833	1 ⊢ ¬ ∃𝑥 ¬ ⊤

This proof depends on syntax axioms:  ¬ wn 3  ⊤wtru 1571  ∃wex 1812

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828

This proof depends on definitions:  df-bi 210  df-tru 1573  df-ex 1813

This theorem is used by:  neutru  36951