Theorem neufal 37321

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

Assertion

Ref	Expression
neufal	⊢ ¬ ∃!𝑥⊥

Proof of Theorem neufal

Step	Hyp	Ref	Expression
1		nexfal 37320	. 2 ⊢ ¬ ∃𝑥⊥
2		euex 2605	. 2 ⊢ (∃!𝑥⊥ → ∃𝑥⊥)
3	1, 2	mto 200	1 ⊢ ¬ ∃!𝑥⊥

This proof depends on syntax axioms:  ¬ wn 3  ⊥wfal 1581  ∃wex 1811  ∃!weu 2596

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-fal 1582  df-ex 1812  df-eu 2597

This theorem is used by:  unqsym1  37340